Bidding strategy for agents in multi-attribute combinatorial double auction

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Expert Systems with Applications xxx (2014) xxx–xxx

ESWA 9731 No. of Pages 28, Model 5G

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Expert Systems with Applications

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Bidding strategy for agents in multi-attribute combinatorial doubleauction

http://dx.doi.org/10.1016/j.eswa.2014.12.0080957-4174/� 2014 Published by Elsevier Ltd.

⇑ Corresponding author. Tel.: +98 31 3793 4510; fax: +98 31 3793 4038.E-mail addresses: fnasirimofakham@yahoo.com, fnasiri@eng.ui.ac.ir

(F. Nassiri-Mofakham), nematbakhsh@eng.ui.ac.ir (M. Ali Nematbakhsh), ahmad-b@eng.ui.ac.ir (A. Baraani-Dastjerdi), aghaee@eng.ui.ac.ir (N. Ghasem-Aghaee),rkowalczyk@groupwise.swin.edu.au (R. Kowalczyk).

URLs: http://eng.ui.ac.ir/~fnasiri (F. Nassiri-Mofakham), http://eng.ui.ac.ir/~ne-matbakhsh (M. Ali Nematbakhsh), http://eng.ui.ac.ir/~ahmadb (A. Baraani-Dastjer-di), http://eng.ui.ac.ir/~aghaee (N. Ghasem-Aghaee), http://www.ict.swin.edu.au/personal/rkowalczyk (R. Kowalczyk).

1 A single sided auction leads to an equilibrium close to the (bid taker) mcompetitive equilibrium outcome (Roh & Yang, 2008)

Please cite this article in press as: Nassiri-Mofakham, F., et al. Bidding strategy for agents in multi-attribute combinatorial double auction. Expert Swith Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.12.008

Faria Nassiri-Mofakham a,⇑, Mohammad Ali Nematbakhsh b, Ahmad Baraani-Dastjerdi b,Nasser Ghasem-Aghaee b, Ryszard Kowalczyk c,d

a Department of Information Technology Engineering, University of Isfahan, P.O. Code 81746-73441, Hezar Jerib Avenue, Isfahan, Iranb Department of Computer Engineering, University of Isfahan, P.O. Code 81746-73441, Hezar Jerib Avenue, Isfahan, Iranc Faculty of Information and Communication Technologies, Swinburne University of Technology, Melbourne, 3122 Victoria, Australiad Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

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a r t i c l e i n f o

Article history:Available online xxxx

Keywords:Bidding strategyBundlingFFM of personalityMarkowitz Portfolio TheorymkNN learning algorithmMulti-attribute combinatorial doubleauctionPackagingTest suite

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a b s t r a c t

In a multi-attribute combinatorial double auction (MACDA), sellers and buyers’ preferences over multiplesynergetic goods are best satisfied. In recent studies in MACDA, it is typically assumed that bidders mustknow the desired combination (and quantity) of items and the bundle price. They do not address a pack-age combination which is the most desirable to a bidder. This study presents a new packaging modelcalled multi-attribute combinatorial bidding (MACBID) strategy and it is used for an agent in either sell-ers or buyers side of MACDA. To find the combination (and quantities) of the items and the total pricewhich best satisfy the bidder’s need, the model considers bidder’s personality, multi-unit trading itemset, and preferences as well as market situation. The proposed strategy is an extension to Markowitz Mod-ern Portfolio Theory (MPT) and Five Factor Model (FFM) of Personality. We use mkNN learning algorithm andMulti-Attribute Utility Theory (MAUT) to devise a personality-based multi-attribute combinatorial bid. Atest-bed (MACDATS) is developed for evaluating MACBID. This test suite provides algorithms for gener-ating stereotypical artificial market data as well as personality, preferences and item sets of bidders. Sim-ulation results show that the success probability of the MACBID’s proposed bundle for selling and buyingitem sets are on average 50% higher and error in valuation of package attributes is 5% lower than otherstrategies.

� 2014 Published by Elsevier Ltd.

1. Introduction

Combinatorial auction (CA) is one of the best suited mecha-nisms for trading a bundle of different synergetic items (goods orservices) in comparison to sequential or parallel auctions. Whenthe items are substitutes, the bidder desires to acquire at mostone of them. However, for the complementary items, the bidder’svaluation for the whole bundle is super-additive; that is, it ishigher than the sum of the bidder’s valuations for the individualitems. Therefore, the more complement the items, the more valu-

able the bundles (Cramton, Shoham, & Steinberg, 2006; De Vries& Vohra, 2003; Milgrom, 2004; Rothkopf, Peke, & Harstad, 1998).

Multi-attribute combinatorial double auction (MACDA) is themost general but complex auction. This combinatorial auctionconsiders other attributes than only price and better satisfies bid-der’s preferences compared to auctions where the bidder is uncer-tain about or uninterested in attribute values that will later besettled during the contract phase (Bichler, Shabalin, & Pikovsky,2009). In addition, while single-side auctions are of interest tothe sellers in the forward and to the buyers in the reverse auc-tions1, double auction clears with fairer outcomes and is of inter-ests to both the buyers and the sellers. A seller can use CA forpromotional offers to customers, since procuring a bundle of itemsrather than individual items can lead to savings in logistics costs,

aximum

ystems

2 F. Nassiri-MofakhamQ1 et al. / Expert Systems with Applications xxx (2014) xxx–xxx

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time, payment and the overall cost savings for the customers, whilethe seller provides packages, which bring him2 the highest returns.A buyer can benefit in CA from efficient allocations when she hassome preferences over combinations of items or a limited budget.Therefore, ‘‘multi-attribute combinatorial double auction’’ can bet-ter answer multi-attribute preferences of both buyers and sellerswhere fair outcomes satisfy synergies among goods that bidders’desire. MACDA has two prominent problems to be addressed:Winner determination (WDP) and bid generation (BGP). Similar toWDP, BGP is also an NP-Hard problem (Park & Rothkopf, 2005;Parkes, 2000; Triki, Oprea, Beraldi, & Crainic, 2014). Bidders wouldlike to benefit for winning the goods. That is, not only a bidder likesto be a winner, but to prevent a winners’ course she/he also prefersto gain rather than loose if she/he wins. Bidding is an importantissue which also affects WDP (Rothkopf & Harstad, 1994;Rothkopf et al., 1998).

In recent years, several bidding strategies have been proposedby studies in combinatorial auctions (An, Elmaghraby, &Keskinocak, 2005; Leyton-Brown & Shoham, 2006; Parkes &Ungar, 2000; Pikovsky, 2008; Triki et al., 2014; Wilenius, 2009).However, none of the existing solutions addresses a multiple-attri-bute, double sided, and multiple-unit bidding scenario together(see Section 2). It is also worth noting that previous studies typi-cally do not model bidder’s willingness to trade a bundle amongmany combinations that can be defined. Some works let the bid-ders to prioritize combinations (Park & Rothkopf, 2005). However,they do not show how the provided packages could be the bestpackage of bundles a specific bidder most prefers. In other words,these studies assume that the bidders must know the desiredbundles and priorities. Moreover, all the bidders in a market arenot willing to be a profit maximizer so that they behave differentlyand prefer different packages. Market history is another source ofinformation that a bidder needs to consider in devising a bid. Thisneed for considering the history of the market and the bidder’sdecision making model for prioritizing the packages makesefficient bidding in one-shot MACDA mechanism a very complextask.

The complexity of bidding a package among an exponentialnumber of potential bundles of items with synergies comes backto the fact that besides the above mentioned requirements, biddersin MACDA should also address several important issues such as (1)size of the package, (2) items to place in the package, (3) quantitiesof each item in the package, (4) attribute values of each item in thepackage, (5) attribute values of the package, (6) price of the pack-age, (7) limitations regarding items’ quantities for sellers, and (8)limitations regarding bidder’s budget for buyers (Leyton-Brown &Shoham, 2006; Vinyals, Giovannucci, Cerquides, Meseguer, &Rodriguez-Aguilar, 2008). Moreover, real markets do not necessar-ily reveal pricing made by all the bidders. The market exposes thebundles along with the prices at which the bundles traded. That is,the market hides individual valuations which each participantassumes for each individual item. The bidder faces the problemof which combination (and quantity) of items and in what valuesfor the package price and attributes is the best combination regard-ing information resources (market history and policy) and his/heritem set and bidding behavior. The bidder’s decision-makingwould depend on the winning/losing risk of the bundles and his/her risk and cooperation attitude towards the market.

This paper addresses the sellers and buyers’ bidding in MACDA.It proposes a strategy for the bidders in order to provide a multi-attribute combinatorial bid (MACBID) that addresses different

2 In this study, from now on, ‘‘she/her’’ and ‘‘he/his’’ refer to the ‘‘buyer’’ and‘‘seller’’, respectively.

Please cite this article in press as: Nassiri-Mofakham, F., et al. Bidding strategywith Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.12.008

behaviors of the bidders in a market. We model a bidder as a per-sonified3 agent that interacts with MACDA by observing a history ofthe previous trades in the market and submitting her/his own bids(ask bids or sell bids) to MACDA in one-shot, where only traded bun-dles (not all the proposed bids) are revealed to the bidders. Thetraded bundle in the history consists of only quantities of each itemin the bundle, values of each package attribute, and the packageprice. A bidder can make personality-based decisions different fromthe other bidders –with even the same item set and valuations – thatobserve the same market trades history. This strategy employs thebidder’s personality, multi-unit item set, and preferences as well asmarket situation. To be informed of the prices of the items and find-ing the most synergetic and desirable package for devising a person-ality-based and market-based multi-attribute combinatorial bid, weextend Markowitz Modern Portfolio Theory (Markowitz, 1952; Prigent,2007), Five Factor Model of Personality (Liebert & Speigler, 1998;McCrae & Costa Jr, 1999; Nassiri-Mofakham et al., 2009; Norman,1963; Oren & Ghasem-Aghaee, 2003), mkNN learning algorithm(Nassiri-Mofakham et al., 2009), and Multi-Attribute Utility Theory(Fasli, 2007; Lewicki, Saunders, & Barry, 2006; Nassiri-Mofakham,Ghasem-Aghaee, Ali Nematbakhsh, & Baraani-Dastjerdi, 2008;Raiffa, 1982; Wooldridge, 2009). Markowitz MPT and FFM of person-ality help the bidder in bundling multi-unit complementary goodsby considering market data as well as the bidder’s item set and per-sonality, while FFM of personality, combinatorial mkNN learning,and MAUT are employed for selecting the best MACBID among sub-stitutes of the devised bundle.

As we focus on the bidding process, issues regarding WDP todesign a complete MACDA mechanism are outside the scope of thisstudy. Therefore, we evaluate the proposed MACBID using bench-marking in a test suite. The study develops a multi-attribute combi-natorial double auction test suite called MACDATS. This test suiteprovides algorithms for generating realistic artificial market data,personality, preferences, and multi-unit item sets of bidders. MACD-ATS which also operates as a support tool in helping humans in effi-ciently devising bids in the complex market, benchmarks efficiency,validation, and confidence of MACBID against other strategies.

The remainder of the paper is organized as follows. We over-view related works in Section 2. In Section 3, we describe the MAC-DA market design space. Section 4 details MACBID strategy andpresents the architecture of bidding agents. MACDATS and evalua-tion of MACBID is presented in Section 5. Section 6 concludes thepaper by summarizing the contributions of the study and outliningfuture avenues of this research.

2. Related work

After the Smith’s seminal work on modeling the market behav-ior in 1962 (Smith, 1962) and reconsidering the importance of bid-ding by Rothkopf and Harstad in 1994 (Rothkopf & Harstad, 1994),several studies have significantly advanced bidding strategies indouble auctions (Gjerstad & Dickhaut, 1998; He, Leung, &Jennings, 2003; Rapti, Karageorgos, & Ntalos, 2014; Vytelingum,Cliff, & Jennings, 2008). In ZI strategy (MacKie-Mason &Wellman, 2006) buyer/seller propose a random offer between thebest bid/ask and the current value. In FM strategy (Tan, 2007)the best bid/ask added with a positive/negative value is proposed.GD strategy (Gjerstad & Dickhaut, 1998) records all bids/asks his-tory and propose a bid/ask by cubic-spline extrapolation for com-

3 We assume the agents emotion-free. By considering emotions motivated fromnotifications and trades history that the participant observes, his/her personalitytraits and then decision-making parameters may change in long term. Dynamicpersonalities exerted temporarily by emotions are not considered in this study. Inaddition, we assume the market is not multi-national and we do not consider culturaldifferences among bidders.

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puting its acceptance probability. Intelligent agents who use AAstrategy (Vytelingum et al., 2008) adjust their short- and long-termbehaviors corresponding to the demand and supply in the market.Although these strategies consider the evolution of a bid duringseveral rounds of the auction, they do not address the initial andeffective bidding in a single-shot auction. Moreover, those worksdo not consider bidding for buyers and sellers who trade bundlesof goods.

In recent years, combinatorial auctions (CAs) have attractedsignificant interests in many disciplines, especially in computerscience, economics, transportation, and electrical engineering. CAsoffer a market mechanism for selling or buying combinations ofsynergetic goods. Despite of single-good auctions with straightfor-ward mechanisms, determining the winners in CAs is a hardoptimization problem (Blumrosen & Nisan, 2007; Cramton et al.,2006; Nisan, Roughgarden, Tardos, & Vazirani, 2007; Peke &Rothkopf, 2003; Rothkopf et al., 1998; Sandholm, 2000; Schwind,2007). Nonetheless, many studies have proposed approximatealgorithms for solving the winner determination problem (WDP)in single- and double-sided CAs (Dang & Jennings, 2003; Fukuta &Ito, 2008; Köksalan, Leskelä, Wallenius, & Wallenius, 2009; Özer &Özturan, 2009; Rastegari, Condon, & Leyton-Brown, 2010;Sandholm, 2002; Schellhorn, 2009; Sureka & Wurman, 2005;Tennenholtz, 2002; Wu & Hao, 2015; Xia, Stallaert, & Whinston,2005). On the other hand, the bidding problem in CAs has recentlyemerged as a focus of attention in many studies as it affects theWDP (An et al., 2005; Bhargava, 2014; Iftekhar, Hailu, & Lindner,2014; Triki et al., 2014; Wang & Xia, 2005; Wilenius, 2009). Studiesproposed for bidding in CAs focus typically on either bid represen-tation (Boutilier & Hoos, 2001; Cerquides, Endriss, Giovannucci, &Rodr guez-Aguilar, 2007; Day & Raghavan, 2009; Goossens,Muller, & Spieksma, 2009; Nisan, 2000; Nisan et al., 2007) or bid-ding strategies. It is worth noting that this study focuses on biddingstrategies and does not consider winner determination and bid rep-resentation problems in CAs. Nonetheless, in the studies in WDP,bids are simply a bundle of random quantity of each item alongwith a price which is assumed as the maximum price the bidderwish to pay. Utility-maximizing and risk-neutrality are the featureswhich have been considered for the bidders in the applications thatemploy single-side combinatorial auctions (Miyashita, 2014;Satunin & Babkin, 2014; Zhong, Huang, Wu, & Chen, 2013).

In works on the bidding problem, some studies consider it jointlywith WDP so that the bidders are involved in solving the problem ofdetermining winners by submitting and revising tentative bids aspart of the global solution (Köksalan et al., 2009; Mendoza &Vidal, 2007). Those solutions are typically derived under strong(and often unrealistic) assumptions regarding the availability ofinformation related to all bidders such as private valuations of otherbidders or tentative solutions. Some other works on bidding in CApropose an adaptive approach for setting the profit margin for bun-dles of bids in the history of bids of a bidder (Sui & Leung, 2008).However, they do not consider which bundle to choose or in otherwords how to choose the items and their quantities for bundling.

The works proposed by Parkes and Ungar (2000), Leyton-Brown, Pearson, and Shoham (2000), Leyton-Brown and Shoham(2006), An et al. (2005), Wang and Xia (2005), Hualong and Fang(2010), Vinyals et al. (2008), Wilenius (2009), Pikovsky (2008),Bichler et al. (2009), address the bidding strategy as a problem iso-lated from solving WDP. The works presented by Wang and Xia(2005) and Wilenius (2009) considerably emphasize on the impor-tance of bidding in CAs. Wilenius analytically shows that a bid onrandom synergetic combination is a best response strategy for bid-ders rather than bids on all combinations. There are two good stud-ies tailored to transportation service procurement which do notmatch with our e-marketplace, but they relate regarding consider-ing combinatorial bid generation. Wang and Xia propose two heu-

ristic approaches for solving the combinatorial bid generation intransportation using integer programming under constraintsregarding the bundle of lanes. A similar work by Triki et al.(2014) solves the same problem in transportation by consideringthe competitors’ prices on bundles and using two heuristics forsequential descending or ascending generation of a bundle basedon approximated pairwise synergy values. It generates stochasticbids, assigns probabilistic prices, and assigns risks regarding thedegree of uncertainty of the bid as to be a winning bundle. Thisstudy not only consider a single side of the market history (thecompetitors’ prices which may not be revealed in realistic mar-kets), but also it model bids using distribution probabilistic func-tions and do not address how a price and by each differentbidder is actually set in the same market.

Most of the works on combinatorial bid generation employs afew computational models which are listed below.

The bestResponse strategy in a game-theoretically analysis foriterative combinatorial auctions is proposed by Parkes and Ungar(Bichler et al., 2009; Parkes & Ungar, 2000; Pikovsky, 2008; Wu &Hao, 2015). In that strategy, the bidder bids for all combinationsthat could maximize his/her surplus given the current prices.Therefore, the enumeration determines the bundle.

Leyton-Brown et al. (2000), Leyton-Brown and Shoham (2006)and Wu and Hao (2015) propose a combinatorial auction test suite(CATS) that attempts to model realistic bidding behavior andaddresses the bidding problem in four domains: Paths in SpaceProblem, Proximity in Space Problem, Arbitrary RelationshipsProblem, and Temporal Matching Problem. The third problem,CATS-3, fits into our e-marketplace scenario and is used as one ofthe benchmark strategies for evaluating our MACBID in Section 6.CATS-3 develops algorithms for generating bundles of single-unitgoods based on the degree of their synergy relationships.

INT strategy (An et al., 2005), which is called bestChain byPikovsky (2008) and Bichler et al. (2009), enumerates the mostprofitable bundle given current prices while the goods have syner-getic relationships.

Nonetheless, the bestResponse, CATS-3 and bestChain strategiesare designed for a single-unit single-sided combinatorial auction.Vinyals et al. (2008) propose a MMUCA test suite adapting CATSfor a special mixed multi-unit combinatorial auction. They do notassume goods in synergy but belonging to different levels in a sup-ply chain. MMUCA also considers discounts regarding multiplicityof items in the bundle. MMUCA is a mixed of reverse and forward(but not a double-side) multi-unit combinatorial auction, while itis designed for a specific multi-level purpose.

However, none of the existing approaches (summarized inTable 1) has addressed a multiple-attribute, double-side, and mul-tiple-unit bidding solution all together. In addition, they do notconsider bidders’ behavior and market information in formulatinga bid. Therefore, the main aim of our research is to develop an effi-cient bidding strategy in a multi-attribute combinatorial doubleauction which considers trading set, bidder personality and marketsituation in a single-shot, sealed bid multi-attribute multi-unitcombinatorial double auction under MACDA policy (Section 3.2)where the participants do not have any information about individ-ual valuation of each participant for each item but the traded pack-age prices.

3. Multi-attribute combinatorial double auction

As a solution for bidding in multi-attribute combinatorial dou-ble auction, we propose MACBID strategy by considering the bid-der’s item set and personality as well as market situation in asingle-shot, sealed bid auction so that no sell bid or buy bid, butonly the trades are revealed to bidders. We consider a bidder asa personalized emotion-free agent who interacts with the market

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Table 1Table showing the state-of-the-art strategies for bidding in CAs.

Strategy Bundle size Bundle goods Goodsquantities

Bundle price Attributevalues

Double-sided

BestResponse Enumeration-based

Bundles with max total surplus – Current price – –

CATS-3 Random Random but Synergetically – Superadditive sum ofvalues

– –

INT Enumeration-based

Those making the highest (private) Synergeticbundles

– Synergetic sum of values – –

MMUCA Random Random from available combinations Random Discount-basedsuperadditive

– –

Fig. 1. Bid representation in MACDA.

5 In the literature, sometimes buy-bid and sell-bid are called bid and ask,respectively. A ‘bid’ is an offer for buying something, while an ‘ask’ is a propose forselling.

6 It is obvious that other attributes are also required for establishing any trade, such

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by observing the history of the previous trades and proposing her/his own bid to the mechanism. However, we do not consider cul-tural differences among the bidders, emotional and commitmentissues. We detail our MACBID strategy in the next section. In thissection, we provide descriptions of the market space.

3.1. MACDA specifications

In MACDA mechanism, that stands for multi-attribute combina-torial double auction, many buyers and many sellers proposemulti-attribute combinatorial bids for trading multiple multi-attri-bute goods based on multiple trade criteria, that is, a multi-attri-bute bundle4 of multi-attribute goods. There are two types ofattributes, one for goods and the other one for packages, namelyitem-based and package-based attributes. Item-based attributes ofa good describe its features, while package-based attributes reflectthe criteria related to trading a package of the goods. This multi-good e-marketplace is also lawful so that in addition to abiding tothe polices of the mechanism (see Section 3.2), all participants knowthe permissible interval of each good attribute value announced by alegal party, e.g., the market maker.

Let nB;nS;nG, and nC are respectively the number of buyers, sell-ers, goods, and package’s attributes in MACDA. Suppose B ¼ fb1; b2;

. . . ; bnBg and S ¼ fs1; s2; . . . ; snSg are sets of buyers and sellers, respec-tively. C ¼ fc1; c2; . . . ; cnCg represents package-based attributes (seeSection 3.2.1). Let G ¼ fg1; g2; . . . ; gnG

g is the set of goods in the mar-ket. MACDA lets different goods to have a different number of attri-butes which again may or may not be the same in types or orders.

For a good g 2 G;Ag ¼ ag1; a

g2; . . . ; ag

� �describes the attributes of

g where nAg is the numbers of g’s attributes. Adopting Nassiri-

Mofakham, Nematbakhsh, Ghasem-Aghaee, and Baraani-Dastjerdi(2006, 2008, 2009a), the value intervals Min validg

1;Max validg1

� �;

Min validg2;Max validg

� �; . . ., and Min validg

nAg;Max validg

h iare

respectively defined for the attributes 1 through nAg . In

addition, ½Min valid1;Max valid1�; ½Min valid2;Max valid2�, . . ., and½Min validnC ;Max validnC � represent the value intervals for pack-age-based attributes. For the quantitative attributes, we assumenvg

1; . . . ;nvgnA

gand nv1; . . . ;nvnC represent the number of values for

goods and package attributes, respectively.

3.2. MACDA polices

MACDA governs several policies regarding bid representation,information revelation, and winner determination. Designing a com-prehensive MACDA mechanism (specially, winner determination)is beyond the scope of this study. Nonetheless, in the followingwe describe these policies on a level required for bidders in design-ing their bids.

4 A package of preferred offers are substitutable bundles where goods in a bundleare complement.

3.2.1. Bid representation policyA multi-attribute combinatorial bid D is an ordered set hd; ei, so

d¼hIg : g 2Gi; Ig ¼hg;qgi and e¼hvðc1Þ;vðc2Þ; . . . ;vðcnC Þi ð1Þ

where, qg and vðckÞ are quantity of good g and the value of kth attri-bute of the package (k ¼ 1; . . . ;nC), respectively. The first element ofDis a set itself containing a combination of multi-unit goods.

In this study, we consider goods with two attributes, namelyprice and quantity. Several quantities can be proposed for goodsin a bundle. All quantities are supposed to be as ‘all-or-nothing’.That is, a trade happens when all quantities offered for goods ina buy-bid and a sell-bid5 are matched. It is worth noting that thereis no item-based attribute ‘Price’ in the bid structure. Price onlyappears for the package representing the synergetic total price ofall goods in this package.

Item-based attributes are not necessarily the same among dif-ferent goods. However, the same attributes have been defined forall packages. For example, suppose a university bookstore in whicha buyer bids for a book and a bag. Item-based attributes for a ‘Bag’can be ‘Size’, ‘Color’, ‘Model’, and so on, while for a ‘Book’, they canbe ‘Title’, ‘Author’, ‘Publisher’, and so on. However, in addition topackage ‘Price’, there are common attributes which are importantin any trade such as ‘Delivery’, ‘Payment Method’, ‘Shipping Style’,‘Packaging Style’, ‘Reputation of the Counterpart’, and so on. Sincegoods are traded in a single package, there is no need for negotiat-ing over these package-based attributes per each good but thepackage. For each good, the same template of attributes is usedamong all participants. However, all attribute values, of eitheritem-based or packaged-based, can be freely different among sev-eral buyers’ bids and sellers’ asks.

A bid in MACDA is represented as in Fig. 1 together with thebidder’s identification6. When bids are submitted to MACDA, theyare time-stamped.

as destination address, account/check/card information, and so on. However, thisinformation will then be exchanged between corresponding parties, if their bids arematched in MACDA. Therefore, there is no need for negotiating such attribute valuesand proposing in the bid.

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3.2.2. Information revelation policyMACDA policy is Partial Information Revelation. Participants pro-

pose sealed bids. MACDA exposes all participants only market his-tory. That is, participants do have information about previoustrades than all offers. This hides asks and bids submitted to MACDAbut trades happened among successful asks and bids. Therefore, allparticipants, either a buyer or a seller, see a sequence of time-stamped trades represented with the same representation andstructure shown in Fig. 1 and Eq. (1). The only difference betweenthe representation of bids in the market and of trades in a transac-tion in the history is that no identification information regardingparties who exchanged those bids is included in the trade archiv-ing. According to Section 3.2.1, trades also include no informationregarding individual good prices but traded package prices. It isworth noting that traded packages in the market history do notnecessarily include the same number and types of goods.

Therefore, MACDA trade history (HMACDA) is an ordered list ofmulti-attribute combinatorial anonymous trades, Dt ¼ ht; dt

; etiwhere,

dt ¼ hItg : g 2 Gi; et ¼ hv tðc1Þ; v tðc2Þ; . . . ;v tðcnC Þi: ð2Þ

In Eq. (2), v tðckÞ is the value of kth attribute of the package(k ¼ 1; . . . ;nC) and dt is a set of ‘multi-unit goods’ It

Itg ¼ hg; qt

gi ð3Þ

where, qtg is quantity of good g exchanged in tth trade. That is, Dt is a

ternary vector of time of the trade, a combination of multi-unittraded goods, and the trade criteria values.

3.2.3. Winner determination policyMACDA is running in one-shots. We assume that it follows an

all-or-nothing method (and based on a time stamp) for determiningwinners and arbitraging (pricing). When one ask and one bidmatch completely, their corresponding bidders win and can trade.If several asks (bids) can match a bid (ask), the earliest ask (bid)wins. Bids and asks continuously are submitted to MACDA. Atthe end of each shot, MACDA clears those bids and asks whichare matched. Designing MACDA winner determination policy as asubject of another stream of the research in CAs is beyond thescope of this study. However, an upper bound for an agent i so thathis/her bid to be supposed as a winning candidate is

pricer P pricei; 8g 2 G; qr

g 6 qig ; if i 2 S

pricer6 pricei

; 8g 2 G; qrg P qi

g ; if i 2 Bð4Þ

where, pricer and qrg are the package’s price and quantities of goods

g in bid r in the market, respectively. Similarly, pricei and qig are the

price of the package and quantities of goods in the agent i’s bid. Ifthe agent’s bid for selling (buying) can satisfy another one’s bidfor buying (selling) according to the condition described in Eq. (4),they then may be supposed as candidate winners.

4. The MACBID strategy

As reviewed in Section 2, none of the existing researches incombinatorial auction has addressed a general solution for multi-ple-attribute, double sided, and multiple-unit bidding. In addition,they do not model bidder’s willingness to trade a bundle amongmany combinations and are unable to show how their providedpackages could be the best package of bundles a bidder prefersmost. It is obvious that such an agent needs to consider bidder’spreferences and behaviors along with observing the market historyand bidder’s item set in devising a bid.

We deal with bidding process in a market that is not multi-national. Therefore, we do not consider cultural differences among

bidders as well as emotional and committing issues. The proposedarchitecture for a personified emotion-free bidding agent considersbidder’s personality, item set, and preferences as well as marketsitu-ation. When a personified bidder who are endowed with an itemset (for selling or buying) participate in MACDA, he/she is beinginformed of MACDA trades history and goods specifications. A bid-der agent faces the problem of which combination of goods and inwhat total price is the best for the bidder to achieve his/her goalsby considering information resources (i.e., market specifications,bidder’s item set, MACDA history and policies) and bidder’s behav-ior. A bidder not only wants to be a winner in MACDA, but also he/she prefers to make a profitable deal. In addition to the marketparameters, his/her decision-making depends on the personalityof the bidder to be a winner. Risk attitude of a bidder will deter-mine how profitable his/her bid may be devised.

Adopting the personality-based bargaining model (Nassiri-Mofakham et al., 2009b) and portfolio optimization (Prigent,2007), we extends Markowitz Modern Portfolio Theory (Markowitz,1952; Prigent, 2007), Five Factor Model of Personality (Liebert &Speigler, 1998; McCrae & Costa, 1999; McCrae & Costa, 1985,1987; Nassiri-Mofakham et al., 2008; Nassiri-Mofakham et al.,2009b; Norman, 1963; Oren & Ghasem-Aghaee, 2003), a combina-torial version of mkNN learning algorithm (Nassiri-Mofakham,Nematbakhsh, Baraani-Dastjerdi, & Ghasem-Aghaee, 2007;Nassiri-Mofakham et al., 2009a), and Multi-Attribute Utility Theory(Fasli, 2007; Nassiri-Mofakham et al., 2009b; Raiffa, 1982) equipagents with decision-making capabilities toward devising a person-ality-based and market-based multi-attribute combinatorial bid.

Using MAUT, a bidder’s choice for a single object is based on thebidder’s preferences represented by a utility function over weightsand values of multiple attributes of the object. According toNassiri-Mofakham et al. (2008) and Nassiri-Mofakham et al.(2009b), this individual choice is best represented by personality-based parameters such as the bidder’s risk and cooperation. In adouble auction, where many buyers and many sellers participatein the market, another type of risk is also raised. This later riskrelates to the valuations of other bidders on the object that causesan uncertainty in their expected returns. When this market is com-binatorial, the uncertainty is increased regarding the complexitiesthat exist in valuations ob bidders on different synergetic combina-tions of goods.

The seminal mean–variance analysis introduced by Markowitz(1952) in quantitative finance shows that investors must take carenot only the returns but also the risk of the portfolio of financialproducts, which is the standard deviation of their portfolio returnthan summation of the products’ risks. Extending the works ofMarkowitz (1952) and Nassiri-Mofakham et al. (2008); Nassiri-Mofakham et al. (2009b) lead us to a personality-based combina-tion selection that considers risks of both the bidder andcombination.

When the bidder is recommended by multi-attribute alterna-tives of a combination of goods, a combinatorial version of mkNNlearning algorithm (mkNN-Com) is developed to show the bidderhigh frequency combination of the attribute values of that combi-nation in the market.

Markowitz MPT and FFM of personality help the bidder in bun-dling complement goods by considering market data as well asbidder’s item set and personality. For making multi-attribute sub-stitute packages from the devised bundle, mkNN-Com learning isemployed. FFM of personality and MAUT then help the bidder forselecting MACBID among these substitutes.

4.1. Architecture of the bidding agent

Fig. 2 depicts the proposed architecture for the bidding agent.The agent has two layers, namely: Perception and Bidding. Through

Fig. 2. Bidding agent architecture.

19 December 2014

Perception layer the agent is being informed of the market as wellas bidder’s endowments and preferences. Bidding is the layerdescribing core of the agent’s bidding strategy.

Perception layer consists of three modules: (1) Information, (2)Preference, and (3) Market Processing. Preference module modelsthe bidder’s behavior, while Market Processing module brings theagent more detailed information about goods traded in the market.These modules are presented in Sections 4.2–4.4.

By detailed information of the market, the Bidding layer pro-vides the agent with abilities in devising a multi-attribute com-binatorial bid by considering both market information andbidder’s preferences via three modules, namely: (1) Bundling,(2) Packaging, and (3) Bid Generation. Bundling and Packagingmodules provides the bidder agent with an optimal multi-attri-bute package based on market situation as well as his/her item

set and preferences. Finally, Bid Generation module determinesthe best multi-attribute combinatorial bid prescribed for thistypical bidder agent. Sections 4.5–4.7 propose these three coremodules.

4.2. Information module

This module contains the information resources that the agent’sbidding is based on, namely: the goods and trade specifications, themarket trades history, and the bidder’s item set.

4.2.1. Goods and trade specificationThe bidder is informed of the set of goods, the attributes of the

goods (item-based attributes), the valid value intervals for each the

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good’s attribute, the package-based attributes, and the valid valueintervals for each package attribute according to Section 3.1.

4.2.2. Market trades historyThe history contains useful information such as the collective

trading behavior of the participants regarding multi-attribute com-binations of goods as well as the degrees of correlation among thegoods in any arbitrary packages. Traded packages anonymously arerevealed to the participants through the information revelationpolicy. HMACDA (MACDA trade history) is an ordered list ofmulti-attribute combinatorial trades HMACDA ¼ hDt : t 2 @i where,

Dt ¼ t; g; qtg

D E: g 2 G

D E; v tðc1Þ;v tðc2Þ; . . . ;v tðcnG Þ� �D E

is defined by MACDA according to Eq. (2). The trades include noinformation regarding the individual good prices but the tradedpackage prices.

4.2.3. Bidder’s item setIn every shot, the bidder agent i trades a package of goods based

on his/her endowments as a set of items. A seller agent sells thegoods available in his stock while a buyer agent buys the goodsthat the bidder needs. Each good in the item set is assigned withthe attribute values. Both agents consider their own bidder’s reser-vation values and other limitations as endowed them by

ItemSeti ¼ Iig : Ii

g ¼ g;RVig

D E; g 2 G

D E: ð6Þ

where, Min validg 6 RVig 6 Max validg .

Bidder’s reservation value is the minimum (maximum) pricethat a seller (buyer) agent is able to submit for the good. A selleragent has another limitation regarding the maximum availablequantities of the good, while a buyer agent should consider tradesin her budget limit. That is,

Limitationsi ¼< Q i

g : g 2 G > if i 2 S

Budgeti if i 2 B

(ð7Þ

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4.3. Preference modeling module

The agent’s preferences include the bidder personality data aswell as her/his decision-making parameters, valuations and desirewith respect to his/her item set. By observing history of the previ-ous trades in the market, the bidder makes personality-based deci-sions that can be different from the other bidder’s who observesthe same market trades history and considers the same item setand valuations.

This module consists of three components that model agent’spreferences regarding the bidder’s valuations for goods, decision-making parameters and objectives.

Fig. 3. Big-five perso

4.3.1. Bidder’s valuationThis component is for evaluating the value of a package and is

applied in Section 4.7.1. In evaluating the value of a bundle ofgoods along with the corresponding trade attributes, we employMulti-Attribute Utility Theory by adopting Nassiri-Mofakham etal. (2008), Nassiri-Mofakham et al. (2006) and Nassiri-Mofakhamet al. (2009b). We suppose the bidder has private utility functionbased on different weighting on each package attribute (criterion).A typical agent i; i 2 B [ S, has two sets containing nC criteria value

intervals and their respective WiC weights, that are

mini1;maxi

h i; . . . ; mini

nC;maxi

h in o; and Wi

1; . . . ;WinC

n o, respec-

tively, which satisfyPnC

C¼1WiC ¼ 1 as well as min validC 6 mini

and maxiC 6 max validC , for all criterion C (see Section 3.1).

Assuming AViC and RVi

C are respectively the agent i’s aspirationand reservation values for any criterion C of the package andei

CðpackageÞ as i’s evaluated score of the value related to criterionC, utility of a package for the agent i is a multi-attribute linearfunction

uiðpackageÞ ¼XnC

WiC � E

iCðpackageÞ ð8Þ

where,

EiCðpackageÞ ¼

eiC ðpackageÞ�RVi

AViC�RVi

C; AVi

C – RViC

1; AViC ¼ RVi

8<: ð9Þ

4.3.2. Bidder’s behavioral parametersIn this study, we suppose the participants with stable personal-

ities. We formalize the behavioral parameters for decision-makingamong emotion-free agents using Five Factor Model of Personalityalso referred to as OCEAN clustered in five groups, namely: Open-ness, Conscientiousness, Extraversion, Agreeableness, and Negativeemotions. Personality of a bidder i is then represented as

Personalityi ¼hOi;Ci;Ei;Ai;Nii

¼ hOi1; . . . ;O

i6i;hC

i1; . . . ;C

i6i;hE

i1; . . . ;E

i6i;hA

i1; . . . ;A

i6i;hN

i1; . . . ;N

D Eð10Þ

so that each personality factor consists six Fuzzy facets as shown inFig. 3. Once the values of the six facets of a personality trait arespecified, the corresponding personality type can be determinedand entered in the personality template in Eq. (10).

The value of a trait is the value of the highest weighted value ofthe six facets, which constitute it. We define the bidder’s Risk fac-tor Rið0 6 Ri

6 1Þ and Cooperation factor CPið0 6 CPi6 1Þ using

Fuzzy Inference Engines adapting the rules defined in Nassiri-

nality template.

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Fig. 4. The agent component for inferencing Risk (R) and Cooperation (CP) of the bidder based on his/her personality (Nassiri-Mofakham et al., 2008, 2009a).

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Mofakham et al. (2008) and Nassiri-Mofakham et al. (2009b) asshown in Fig. 4. Sections 4.5.1 and 4.7.2 employ this component.

4.3.3. Bidder’s objective functionIn the previous work on personality-based bargaining model

(Nassiri-Mofakham et al., 2009b), proposing the best initial offerin the bilateral negotiation (where the agent has not yet receivedany information from his/her counterpart) is according to the bid-der’s risk-based boundary utility values. However, in this market,the bidder agent is informed of the market trades history and he/she makes his/her best decision regarding both the risk- and coop-eration-based values in single-shot.

Different bidders may prefer different combinations withrespect to their personalities. That is, besides maximizing thereturn and minimizing the risk, maximizing return-risk or any othervarieties are the objective functions a bidder can employ in select-ing an optimal combination. Therefore, by adapting (Rom &Ferguson, 1994) we define the goal and objective of the biddertoward selecting a bundle of goods by introducing an RLi factor(0 6 RLi

6 1) as

RLi ¼ dðRi;CPi;aiÞ ð11Þ

where,

dðRi;CPi;aiÞ ¼ Ri þ aiCPi

1þ aið12Þ

is the decision function and 0 6 a 6 1 is a concentration parameterthat determines the weight of the bidder’s Risk and Cooperationfactors. Ri; CPi and ai influence the interval that RLi falls in, its posi-tion in the interval, and the length of the intervals, respectively. Thesmaller is the ai, the shorter are the intervals, and vice versa. RLi

plays a role in the bidder’s decision-making based on the returnand risk of a combination of goods (see introduction of Sections 4and 4.5.3) as formulated below:

f iðcombinationÞ ¼ RLireturnCombination � ð1� RLiÞriskCombination: ð13Þ

RLi represents the bidder’s degree of rationality regarding a combi-nation. A purely rational bidder agent with the minimum RLi fol-lows the maximum return combination (Rom & Ferguson, 1994),while the most risk-aversive agent who has the maximum RLi fol-lows a combination with a minimum risk (Rom & Ferguson, 1994).

Then after, the bidder i solves the problem using Simplexmethod for the objective function that is then defined as

max f iðcombinationÞs:t: CONSTRAINTSi are satisfied

ð14Þ

where, CONSTRAINTSi are defined as Sections 4.5.3 and 4.5.4. Thiscomponent is applied in Sections 4.5.3 and 4.7.2.7

7 Fo r a agnet f o l lo wing the max i mum ret u rn , the funct ion i smax returncombination

s:t: CONSTRAINTSi are satisfied, w h i l e a r i s k - a v e r s i v e a g e n t s o l v e s

min riskcombination

s:t: CONSTRAINTSi are satisfied.

4.4. Market processing module

Through Information module, the bidder is informed of thegoods and the values of their attributes along with a total packageprice traded previously in the market based on related packageattribute values. In proposing a bid, the bidder needs to find whichgoods and in what quantities he/she should place in the bundleand in what a total price and attribute values propose to the mar-ket. However, for generating and pricing such a bundle, the bidderfirst needs to price goods in his/her item set. As described in Sec-tions 3 and 4.2, the bidder has no information regarding individualvalues of the goods from the synergetic packages traded in themarket. By using Market Processing module, the bidder gains anestimation of these unit prices.

4.4.1. Filtering HMACDAFor calculating an optimal multi-attribute combinatorial bid, a

bidder agent solely considers transactions that include at leastone good from his/her ItemSeti (see Eq. (6)). The agent vertically fil-ters MACDA trade history (HMACDA) using an association of allgoods in his/her ItemSet. In this way, the bidder agent processesFMACDA (filtered HMACDA) containing a sequence of limitedamount of data logs in a period of time. That is,

FMACDA ¼ hDt jDt ¼ ht; dt; eti 2 HMACDA; 9g; g 2 Ii

g ; g 2 Itg

: Iig 2 ItemSeti; It

g 2 dti ð15Þ

where, dt and Ig are defined as Eqs. (2) and (3), respectively.The bidder agent then horizontally extracts random transac-

tions from FMACDA. This extraction is based on a partitioningparameter q that determines which percentage of FMACDA trans-actions is used as the training set for the agent. This sampling gen-erates TMACDA and VMACDA. TMACDA is used for the agentbidding purposes. In Section 5.3, we then employ VMACDA for test-ing and validation of the agent’s bid.

4.4.2. Predicting individual goods’ pricesFor a bidder agent who only knows the individual reservation

value of the goods in his/her ItemSet, it is not easy to preciselyassign a synergetic value to their combinations, however. It is use-ful to find how the other participants have valued synergies of acombination. Individual prices for the goods along with the pack-age price can give the agent a good idea for evaluating the synergy.However, TMACDA provides the agent with information related tothe traded packages rather than prices of the individual goods (seebid representation and information revelation policies in Sections3.2.1 and 3.2.2).

The bidder considers the prices of packages and the goods’quantities. For finding the best combination of the goods that thebidder has in his/her ItemSet, the agent makes a decision basedon the trading situation of the prices of individual goods tradedpreviously. However, these are hidden information revealed to noparticipants. From Section 3.2 it is remembered that participants

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Fig. 5. Iterative sliding window method for predicting goods’ individual prices.

Fig. 6. Reducing dispersions from predicted unit prices.

19 December 2014

also keep this information private and do not reveal to MACDAeither.

To predict these hidden individual prices, suppose M¼ jTMACDAj = the number of trades in TMACDA and N 6 nG is themaximum single-item number of goods traded in TMACDA8, whereM � N. Therefore, by considering only the package price and quan-tities of the goods traded in each package, the seller should solve asystem of Mequations and M � N variables as

q11p11 þ q12p12 þ � � � þ q1Np1N ¼ p1

q21p21 þ q22p22 þ � � � þ q2Np2N ¼ p2

qM1pM1 þ qM2pM2 þ � � � þ qMNpMN ¼ pM

ð16Þ

where prgðr ¼ 1; . . . ;M; g ¼ 1; . . . ;NÞ is the hidden single-item pricesupposed for good g in transaction package r and pr is the price ofthe package traded in this transaction. By getting a slice of N equa-tions of the system, we still have N � N variables and N equations.The system is highly constrained and has no solution for N > 1.Although, single-item prices have fluctuations over the marketdue to different trading behaviors of participants, in MACDA with

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8 If we suppose jItemSetj is the single-item number of goods in the bidder’s ItemSet,it is worth noting that N is neither necessary equal to nG nor jItemSetj. AlthoughTMACDA contains no ‘null transaction’, it may contain transactions with ‘null goods’. A‘null-transaction’ is a transaction which contains no goods in consideration ((Han &Kamber, 2006) A ‘null good’ is a good which is not under consideration. For a bidder,those goods in a traded package which are not available in his/her ItemSet are called‘null goods’.

behavior of a double auction, they vary around equilibrium-like val-ues. By taking this assumption, therefore, we reduce Eq. (16) to asystem of N variables pg (goods equilibrium prices), g ¼ 1; . . . ;N.This is similar to substituting prg ’s by an average of prg ’s.

However, for employing Markowitz Portfolio Theory(Markowitz, 1952) described in the introduction of Section 4, weneed a full history rather than a single (average price) solution.This also helps for increasing the accuracy of the result and takinginto account the price variances. We present an Iterative SlidingWindow method to solve this problem as described below.

Iterative Sliding Window Method. In this method, we iterativelyslide a window of N equations toward the end of TMACDA, as

shown in Fig. 5. Among all MN

� , this solves

PM�Nþ1k¼1 ðM � N

þ2Þ � k systems of size N. That is, we get at mostðM � N þ 1Þ � ðM � N þ 2Þ=2 solutions (i.e., products’ pricecombinations)9.

It is worth noting that not all these systems has valid solutions.Solutions containing positive prices for all N goods build PMACDAcomposed of a new stream of transactions based on these individ-ual goods’ prices. Windows containing newer transactions createnewer price combinations while those including older transactionscompose older combination of prices. Therefore,

9 For example, considering an ItemSet containing four goods reduces a period ofHMACDA with 1000 transactions into TMACDA with M ¼ 880. Thus, we get at most(880 � 4 + 1)⁄(880 � 4 + 2)/2 = 385,003 solutions (price combinations).

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PMACDA ¼ hr; hprg : g ¼ 1; . . . ;Ni : r 2 @i: ð17Þ

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4.4.3. Reducing price dispersionsIn predicting the prices using Iterative Sliding Window Price

Prediction method (Fig. 5), PMACDA contains all non-negativesolutions. PMACDA is used as a stream of the goods’ prices tradedover a period of time. With respect to real private prices for thegoods traded in packages in double-sided mechanism experiments,although PMACDA provides pretty good average informationregarding goods prices, these prices may contain huge dispersions.Filtering PMACDA throws out dispersed data and improves STD ofthe predicted values. We carry out this filtering using an e-Test byadapting to F-test over data. F-test says that if by eliminating atransaction we get F ¼ std2

new=std2old close to 1, then removing that

transaction is useful; however, if F gets larger than 1, then thetransaction should not be removed. In the following, we presentour e-Test.

e-Test methodWe first compute lg , the mean of the variables pg (prices of

good g) as lg ¼ 1K

PKg¼1pg , where K ¼ jPMACDAj is the number of

transactions created in PMACDA. Following Section 4.4.2, N 6 nG

is the maximum single-item number of the goods (item types)traded in PMACDA. It is worth noting that vectors representingtransactions in PMACDA contains the same number of goods asTMACDA. However, PMACDA and TMACDA differ in the numberof transactions either.

We assume e is the error rate tolerated in predicting pg ’s. Weiteratively test each transaction in PMACDA to throw out transac-tions with large dispersions in the predicted prices. In this filtering,we eliminate a transaction if the deviation of at least one pg in thetransaction exceeds e percent from its lg . That is, if for any pg in a

transaction in PMACDA we observe jpg�lg jlg

P e, then this transaction

is not entered into FPMACDA (filtered PMACDA). Fig. 5 depicts thisfiltering method.

Using this filtering, the bidder agent now has a good estimationof the market prices in FPMACDA. These prices have been predictedonly based on traded quantities of the products in combinatorialtransactions in a total package price. The method interestinglyresulted in predictions close to real prices regarding their standarddeviation rg . These values are bidder-independent so that all bid-ders observing the same period of the market history estimate thesame averages and standard deviations for the same goods.

4.4.4. SqueezingGenerated FPMACDA now contains prices of all goods in trans-

actions addressing trades that consist at least one good in theagent’s ItemSeti. However, the agent only needs prices related tothose goods in his/her ItemSeti. Therefore, the agent squeezesFPMACDA by throwing out unrelated prices to produce SMACDA as

SMACDA ¼ hr; hprg : g 2 ItemSetii : r 2 @i: ð18Þ

This squeezed FPMACDA, has the same number of transactions asFPMACDA and with the same number of goods in ItemSeti.

4.5. Bundling module

As explained in Section 4.1, Bundling, Packaging, and Bid Gener-ation are the core modules for the bidder agent in devising a bid. Inthis section, we detail Bundling module by proposing four compo-nents for pricing the goods in ItemSet, interpreting the utilizationof the market for the prices set by the agent, finding optimal bun-dle of goods and their quantity percentages in the bundle, andfinally quantifying the goods’ quantities and the bundle price.

4.5.1. Preference- and market-based unit-pricing modelThe bidder agent now should set a price for each good as if it is

for trading individually than in a combination. The agent shouldcompute these individual prices according to the bidder’s prefer-ences as well as the market situation. By employing Market Pro-cessing module in Section 4.4, the bidder agent has found anestimation through average lg and standard deviation rg of mar-ket prices for each good g in his/her ItemSet. In Section 4.3.2, weformulated behavior of the agent toward risk and cooperation inthe market using the bidder’s personality factors. In addition,through Section 4.2.3 the agent is informed of the bidder’s reserva-tion values for each good.

In our previous work (Nassiri-Mofakham et al., 2009b), propos-ing the best initial offer in bilateral negotiation in a single-good e-marketplace where the agent has not yet received any informationfrom his/her counterpart is according to the bidder’s risk-basedboundary utility values. However, in MACDA, the agent is informedof previous transactions in the market. Therefore, his/her decision-making in single-shot is based on both risk- and cooperation-basedvalues. Hence, we extend that approach (Nassiri-Mofakham et al.,2009b) to a wider range of behaviors for the bidders interactingthe market by considering Risk (Ri) and Cooperation (CPi) of eachbidder i and his/her reservation values RVi

�as well as average

lg and standard deviation rg of market prices for each good g.The bidder agent i generates a price set for all goods g in his/herItemSeti as

PRICINGi ¼ hg; pricingig : g 2 ItemSetii ð19Þ

where,

pricingig ¼ uðiÞYi

g þ ðuðiÞ þ ð�1ÞuðiÞe�bCPi ÞXig ð20Þ

Xig ¼ Fi dXi

g ;DXig

�; Yi

g ¼ Fi dYig ;DYi

�; b ¼ ln

!ð21Þ

so that,

FiðÞ ¼MaxðÞ if i 2 S

MinðÞ if i 2 B

�ð22Þ

while, dXig ;DXi

g and dYig ;DYi

g are computed using ri

ri ¼ ð�1ÞuðiÞðRi �uðiÞÞ ð23Þ

where,

uðiÞ ¼0 if i 2 S

1 if i 2 B

�: ð24Þ

We also employed

dig ¼ ð�1ÞuðiÞrg ð25Þ

that aggregates the seller and buyer agents’ pricing formula.Fig. 7 presents this pricing algorithm for both seller and buyer

agents in MACDA. In this pricing, a unit price pricingig is proposed

with respect to the distance of CPi and Ri with those of extremebehaviors. These extreme prices Xi

g and Yig are first determined

through Ri and then adjusted by CPi. Without any regard to thedegree of risk and cooperation of a bidder agent, seller and buyeragents prefer higher and lower prices, respectively. Accordingly,they employ Max and Min functions in setting a price by consider-ing both the bidder’s RVi

g and market prices, respectively.It is worth mentioning that the approach presented in Fig. 7

encapsulates 10 class of scenarios regarding RVig of a bidder i for

good g with respect to its lg and rg in the market. Five classes rep-resent scenarios for pricing by a seller agent whose Ri value variesbetween 0 and 1. In each class, CPi value of the seller agent belongs

Fig. 7. The preference- and market-based pricing algorithm.

19 December 2014

to a region for values between 0 and 1 (as shown in the firstcolumn of Fig. 8). Similarly, five classes of scenarios represent thebuyer agent’s pricing method. When the seller agent’s Ri falls intothe interval [0.45,0.55], different pricing with respect to his/her CPi

are as shown in Fig. 8.We explain the approach using Fig. 9 and assuming that bidder i

is a seller agent. This seller agent considers different values inhis decision-making. For example, in Scenario 9(b), these valuescorresponding points 1–7 are as follows:

Point 1: lg þ rg and Max lg þ rg ;RVig

�Point 2: Avg lg þ rg ;RVi

�Point 3: lg and Max lg ;RVi

�Point 4: Avg lg ;RVi

Fig. 8. Scenarios for pricing a good g by

Point 5: RVig and Max lg � rg ;RVi

�Point 6: Avg lg � rg ;RVi

�Point 7: lg � rg

Therefore, for a seller agent with this RVij, when Ri ¼ 0:50 and

CPi ¼ 0:85, two extreme prices affecting his pricing are

Xig ¼ Avg lg ;RVi

�at point 4 and Yi

g ¼ RVig at point 3 that corre-

spond to CPi ¼ 0 and CPi ¼ 1 for sellers with 0:45 6 Ri6 0:55,

respectively (See ComputeExtremePrices in Fig. 7 where this seller

agent with Ri ¼ 0:50 falls in the third case 0:45 6 Ri6 0:55). Hence,

this seller agent assigns pricingig ¼ Avg lg ;RVi

�e�0:85 ln

Avg lg ;RVigð Þ

RVig to

good g.

seller agents with 0:45 6 Ri6 0:55.

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Table 3Unit-Pricing for a ‘shirt’ by eight buyer agents in a market with lshirt ¼ 52:38 andrshirt ¼ 8:02.

Buyeragent i

1 2 3 4 5 6 7 8

Ri 0.50 0.83 0.50 0.83 0.50 0.83 0.50 0.83

CPi 0.85 0.85 0.15 0.15 0.85 0.85 0.15 0.15

RVishirt

45 45 45 45 55 55 55 55

pricingishirt

45.00 45.00 45.00 45.00 53.89 55.00 54.81 55.00

Fig. 9. Four scenarios of RVig of bidder i for good g with respect to its lg and rg in the market.

19 December 2014

Example 1. As a more detailed example, suppose seller agent 1

with R1 ¼ 0:50 and CP1 ¼ 0:85 would like to price a shirt whose

reservation value is RV1shirt ¼ 45 while lshirt ¼ 52:38 and rshirt=8.02.

Therefore, he proposes pricing1shirt ¼ Avgð52:38;45Þe�0:85 lnAvgð52:38;45Þ

¼ 45:54. However, seller agent 2 who has endowed shirts with the

same reservation value RV2shirt ¼ 45 but with R2 ¼ 0:83 and CP2

¼ 0:85, prices his shirts differently and higher than of seller agent 1

as pricing2shirt ¼ Maxð52:38;Avgð60:40;45ÞÞe�0:85 lnMaxð52:38;Avgð60:40;45ÞÞ

Avgð52:38;45Þ

¼ 49:27. Table 2, shows the pricing of only eight different agents(among all) for selling shirt in this market. j

It is worth noting that, for the same endowments of ItemSets,the seller agent with Ri ¼ 1 is the most aggressive seller agentwho prices the maximum value for the good, while a selleragent with Ri ¼ 0 shows the most submissive behavior and setsthe good with the minimum possible price. For cooperation factor,it is conversely. That is, for two seller agents with the same risk fac-tors, the seller with CPi ¼ 0 has the least cooperation while theother seller with CPi ¼ 1 is the most cooperative seller. Therefore,a seller agent with Ri = 1 and CPi = 0 shows the most aggressivebehavior while the most submissive seller is the agent withRi ¼ 0 and CPi = 1. A submissive seller is worried about losing thecurrent shot for selling his ItemSet, while an aggressive seller agentis greedy to attain the maximum profit in the shot.

The following example repeats Example 1 for buyer agents.

Example 2. It is obvious that a buyer’s reservation value (themaximum value that she can pay for a good) may or may not behigher than a seller’s reservation value (the minimum value that hecan sell the good at). However, for comparing the approachpresented in Fig. 7 and showing that different roles may causedifferent pricing, we suppose eight buyer agents with the samevalues of the seller agents in Example 1. Table 3 shows prices thatthese buyer agents (among all) assign to their required shirt. �

Table 2Unit-Pricing for a ‘shirt’ by eight seller agents in a market with lshirt ¼ 52:38 andrshirt ¼ 8:02.

Selleragent i

1 2 3 4 5 6 7 8

Ri 0.50 0.83 0.50 0.83 0.50 0.83 0.50 0.83

CPi 0.85 0.85 0.15 0.15 0.85 0.85 0.15 0.15

RVishirt

45 45 45 45 55 55 55 55

pricingishirt

45.54 49.27 48.12 52.10 53.00 55.40 55.00 57.29

4.5.2. Interpreting the marketThe bidder agent i now has priced goods g; g 2 ItemSeti using Eq.

(20). To bid optimally, the bidder needs to explore how profitablethe market situation is regarding the prices he/she assigned for his/her ItemSet compared to prices of the goods traded in the market.To find high return products, the bidder interprets returns thatcould gain from the market history per estimated transactionprices.

Suppose that the bidder desires to trade a good g in pricingig . By

observing transaction r in the market history, where the good g hasbeen traded at price pr

g , we define

returnig pr

g ; pricingig

�¼ð�1ÞuðiÞ pr

g � pricingig

�pricingi

ð26Þ

where uðiÞ is defined as Eq. (23).Now, the bidder can interpret SMACDA transactions (See Sec-

tion 4.4, Eq. (16), Fig. 6, and Section 4.4.4) into IMACDAi based onthe return percentages that he may gain by trading his/her goodsat those transaction prices. IMACDAi is then represented as

992992

IMACDAi ¼ hr;RETURNri : r 2 @i ð27Þ

where,

RETURNri ¼ hreturni

g prg ; pricingi

�: g 2 ItemSetii ð28Þ

and r is the sequence number of IMACDAi transactions.It is worth noting that this interpretation of SMACDA transac-

tions is carried out only for those goods that are exist in ItemSeti.That is, IMACDAi has the same number of transactions as SMACDAbut contains less number of goods as equal as of goods in ItemSeti.

10071008

10101010

10161017

10191019

10201021

10231023

10241025

10271027

10511052

10541054

10551056

10581058

10591060

10621062

10631064

10661066

1080Q3

19 December 2014

4.5.3. Devising optimal combination of goodsFollowing Sections 4.4.1–4.4.4, 4.5, 4.5.1 and 4.5.2, the bidder

now has individual return values regarding predicted individualgoods prices. Based on these return values, we design a combina-tion, which is the most profitable one for the seller. To do that, wecan now employ an approach based on Markowitz Portfolio Theory(Elton & Gruber, 1997; Fama, 1971; Goebel, 2007; Markowitz, 1952;MÜLler, 1988; Prigent, 2007), as follows.

For each good g; g 2 ItemSeti, the expected return of the good forthe bidder i is

Eig ¼

returnig pr

g ;pricingig

�; Ki ¼ jIMACDAij ð29Þ

where, variable returnig is defined as Eq. (26). We suppose non-neg-

ative qig ’s initialized equally are quantity percentages corresponding

goods g in a combination for bidder i, so thatPNi

g¼1qig ¼ 100 where,

Ni is the number of goods in the bidder’s ItemSeti. Return of a com-bination of goods is then defined as the sum of weighted expectedreturns of goods as

returnicombination ¼

WEig ; g 2 combinationi ð30Þ

where,

WEig ¼ Ei

g � qig ð31Þ

is the weighted expected return of good g and

combinationi ¼ hqig : g ¼ 1; . . . ;Nii; returni

combination; riskicombination

D Eð32Þ

includes quantity percentages corresponding goods composing thecombination as well as return and risk of combination as definedin Eqs. (30) and (34), respectively.

Now, using a Simplex optimization the bidder finds which goodsand in what quantity percentages maximize his/her objective func-tion10 (e.g., with maximum return in a minimum risk. See also Eq.(11) in Section 4.3.3) regarding a combination.

Several constraints are applied in the optimization with respectto quantity percentages weighted returns of goods, as follows.Constraint 4 is considered in Section 4.5.4.

Constraint 1. All quantity percentages must be non-negative:8g 2 ItemSeti; qi

g P 0. j

g¼1qig ¼ 100. j

10941095

10971097

Constraint 3. Weighted returns of goods must be non-negative:8g 2 ItemSeti;WEi

g P 0. j

For the most profitable bid, the bidder likes to choose a combi-nation, which maximizes his/her objective function (see Section4.3.3). For example, a bidder may prefer a combination, whichgives him/her the highest return with a minimum variance com-pared to any other combinations. Variance of a combination is cal-

10 In this study, each bidder solves his/her optimization problem using his/her fixedobjective function to provide a single combination which is later enlarged to apackage of multi-attribute bundles in Section 4.6. However, if the bidder changes thevalue of a for more concentrating his/her goal toward either return or risk in Eq. (11),he/she can gain a list of combinations sorted by their objective values. Some of thesecombinations may be iso-variance while the others may be iso-return. Iso-variancecombinations are substitutable for a bidder which employs max(return) as his/herobjective function. Similarly, a bidder that would like to choose a combination withthe greatest possible rate of return, are indifferent among iso-return combinations.

culated from the weighted individual goods variances and theircovariance from (predicted) historical price data in IMACDA.Goods’ variance/covariance matrix is defined as

VCVi ¼ vcv ig;h

h iN�N¼

vari1 covi

1;2 � � � covi1;Ni

covi2;1 vari

2 � � � covi2;Ni

. ... . .

coviNi ;1

coviNi ;2

� � � variNi

26666664

37777775

ð33Þ

in which, variance and covariance of goods g and h are

varig ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

Ki � 1

r¼1returnr

g � Eig

where; Ki ¼ jIMACDAij

covig;h ¼

returnig � Ei

�� returni

h � Eih

�vari

gvarih

respectively. Therefore, variance of combination is defined as

riskicombination ¼ vari

combination ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi

h¼1vcv ig;h �qi

g �qih

; g;h2 combinationi:

ð34Þ

Variance of a combination is equated with risk, measuring howmuch worse than average the combination return are likely to be.Optimal portfolio then decreases this uncertainty in gaining higherlevels of returns by minimizing volatility in combination return. Bycombining higher return goods in a smart way, their fluctuationscancel each other out. This gives the bidder high average rate ofreturn, with less of fluctuations.

When the market growth situation is unknown, it is rational toselect a combination composing goods less correlated with respectto their returns. It is useful for participants in devising their initialbids for entering the market. Next, when the bidder explores theefficiency of the market, he/she can focus on combinations con-taining high correlated goods, which yield higher returns thoughin higher risks. This issue is considered in Section 7.2 for furtherresearch.

4.5.4. Optimal bundle generationBy optimization presented in Section 4.5.3, the bidder does now

have an optimal combinationi as defined in Eq. (32). This sectionintroduces a component that converts values of quantity percent-ages and rate of return to values of goods quantities and packageprice to provide the bidder with an optimal bundle of goods. Todo that, the bidder agent first needs to have a look at his/her Item-Set Limitationsi. In the following, we quantify the values from theseller and buyer agent points of view.

(a) Bundling for the seller agentFor converting values of quantity percentages to values of goods

quantities, suppose qi is the total number of quantities in the bun-dle. Therefore, quantityi

g corresponding goods g in the bundle is

quantityig ¼ qi

g � qi ð35Þ

where qig , defined through Eq. (32), are quantities corresponding

goods g in combinationi. However, according to Eq. (7), a seller agentshould consider the maximum available quantities correspondinggoods g in the his ItemsSeti;Qi

1;Qi2; . . . ;Qi

Ni , where Qig P 0; g

¼ 1; . . . ;NiðNi is the number of goods in the bidder’s ItemSetiÞ.

Constraint 4S. The seller agent i should obviously considerquantityi

g for goods g that quantityig 6 Qi

To be attainable for existing goods, therefore the seller agentmust have

11091109

11101111

11131113

11161117

11191119

11271128

11301130

11311132

11341134

19 December 2014

qi ¼minQ i

: g ¼ 1; . . . ;Ni; qig – 0

Therefore, the bundle costs

pricei ¼XNi

quantityig � pricingi

g ð36Þ

where pricingig are defined as Eq. (20) in Section 4.5.1.

Therefore, the combinatorial bundle of multi-unit goods pre-scribed for the seller agent i is

CBundlei ¼ hhquantityig : g ¼ 1; . . . ;Nii; priceii ð37Þ

where quantityig and pricei are defined as Eqs. (35) and (36),

respectively.(b) Bundling for the buyer agentSimilar to a seller agent, a buyer agent applies Eq. (35) for con-

verting values of quantity percentages qig corresponding goods g to

goods quantities values quantityig assuming qi is the total number

of quantities in the bundle. Therefore, the bundle should cost lessthan or equal to her budget. That is,

pricei ¼XNi

quantityig � pricingi

g 6 Budgeti ð38Þ

which is reduced to

Budgeti

100PNi

g¼1qig � pricingi

: ð39Þ

However, the buyer agent now should consider Constraint 4B forpricei.

Constraint 4B. It is obvious that the buyer agent i should considera bundle whose pricei satisfies pricei

6 Budgeti. h

Therefore, quantityigðg ¼ 1; . . . ;NiÞ are defined using Eqs. (35)

and (39). pricei is then determined through Eq. (38). This leadsthe buyer agent i to a combinatorial bundle of multi-unit goodsCBundlei as defined in Eq. (37).

4.6. Packaging module

Four components of Bundling module provided the bidderagent with CBundlei, a combinatorial bundle of multi-unit goods.By this end, this optimal combinatorial bundle is a single-attributepackage only considering the price attribute of the package.

Packaging module now assigns values of other package-basedattributes for wrapping a bid. This wrapping is based on market

Fig. 10. Generating confident trad

data to generate substitute packages. Section 4.7 then filters thesesubstitutes using bidder’s preferences.

For this packaging, we consider two cases. First, we consider 2-attribute packages, where the second attribute is for example onlyone of ‘Delivery’, ‘Payment Method’, ‘Shipping Style’, ‘PackagingStyle’, ‘After Sale Services’, ‘Reputation of the Counterpart’ attri-butes. This case utilizes Multi-Valued k-Nearest Neighbor Learningalgorithm (Nassiri-Mofakham et al., 2009a). Next, we present analgorithm for packaging multi-attribute packages where any num-ber of package-based attributes can be considered.

To do that, the bidder agent first does a c-Test on FMACDA toreduce it to a CFMACDA that contains confident transactions.

4.6.1. Filtering confident history tradesIn order to have an accurate prediction of package-based attri-

butes values for the recommended CBundlei, we limit the bidderagent to confident historical transactions in TMACDA using a c-Test. A confident transaction is a transaction that is exactlymatched with the CBundlei template. That is, it contains exactlythe same items as CBundlei. Note that TMACDA consists transac-tions that contain at least one good g; g 2 ItemSeti.

c-Test. For this filtering test, quantityig in CBundlei are XOR-ed

with quantities of goods in each of K transactions in TMACDA(K ¼ jTMACDAj). If quantityi

g > 0 and no quantity of good g has beentraded in transaction t or if quantityi

g ¼ 0 and transaction t hastraded good g, then transaction t is not entered into CTMACDA.Fig. 10 depicts this filtering method for generating confidenttransactions.

4.6.2. Packaging in multi-attribute combinatorial e-marketplaceThis section provides the bidder agent with a package of bundles.

This package contains substitutable attribute values highly co-occurred in the market trades history regarding the bundle. We firstintroduce this packaging in 2-attribute combinatorial e-market-place. The multi-attribute case is then presented by proposing acombinatorial multi-valued k-nearest neighbor learning algorithm.

2-Attribute combinatorial packaging. For 2-dimensional pack-ages, Multi-Valued k-NN learning algorithm (Nassiri-Mofakhamet al., 2007; Nassiri-Mofakham et al., 2009a) is applied for deter-mining m substitute values highly occurred in the trades history(CTMACDA) based on the second attribute of the package (It isworth noting that the first attribute is price that was determinedby Bundling module). These m (m is variable) values of this pack-age-based attribute have highly occurrences among the k nearesttrades neighbor (Cover & Hart, 1967; Han & Kamber, 2006;Mitchell, 1997) to the queried package with respect to its item-based attributes. The mkNN algorithm presents multi-valued clas-

ing history based on CBundlei .

12021202

121812201220

12331233

12651266

12681268

19 December 2014

sification for an instance based on a single query (e.g., ‘‘paymentmethod’’ package attribute). In other words, a multi-dimensionalinstance (multi-good bundle) is considered for classification inanother multi-dimensional space (multi-attribute space). There-fore, the bidder agent is prescribed with

2ACPACKi ¼ hhquantityig : g ¼ 1; . . . ;Nii;pricei

; fv1; . . . ;vmgið42Þ

where v1; . . . ;vm are m values of this package attribute that havehigh occurrence rate among k nearest (with respect to their Euclid-ian distance) trades to CBundlei.

Example 3. Assume CBundlei ¼ h4 pairs of Shoes; 4 Bags; 8Shirts; 8 Trousers; 2000i is the optimal combinatorial multi-unitbundle recommended to the bidder agent i in a 2-ttributecombinatorial e-marketplace, where the package-based attributesare Price and Payment Method. Among all transactions inCTMACDA, suppose mkNN learning (with k = 9) first explores ninetransactions shown in Table 4 as 9-nearest neighbors of CBundlei.Among ‘‘Credit’’, ‘‘Check’’, and ‘‘Cash’’, it then recommends ‘‘Credit’’and ‘‘Check’’ as both are highly occurred values of Payment Methodattribute for packaging (with equal occurrence rate of 4/9). Bythese m = 2 values recommended by mkNN learning, the bidderagent is now prescribed with

2ACPACKi ¼hh4 pairs of Shoes; 4 Bags; 8 Shirts; 8 Trousers; 2000i; fCredit;Checkgi: �Multi-Attribute Combinatorial Packaging. For multi-attribute

packages, where an instance is queried based on several ‘interre-lated’ classes (e.g., ‘‘payment method’’ and ‘‘delivery’’ packageattributes), we need an algorithm that determines multiple substi-tute alternative package bids, while it also considers interdepen-dencies among package-based attributes.

In this section, we extend mk-NN learning algorithm for multi-classifying a queried instance in determining combination of val-ues which may co-occur for its package-based attributes. There-fore, the bidder agent is then prescribed with

MACPACKi ¼ hhquantityig : g ¼ 1; . . . ;Nii;pricei

fhv1ðc1Þ; . . . ;v1ðcnC Þi; . . . ; hvmðc1Þ; . . . ;vmðcnC Þigi ð43Þ

where m and hvwðc1Þ; . . . ;vwðcnC Þi, w ¼ 1; . . . ;m, are determinedusing mkNN-Com Learning Algorithm. A hvwðc1Þ; . . . ;vwðcnC Þi is anordered set consisting a combination of values of attributesc1; . . . ; cnC that have highly co-occurred with each other in the tradeshistory (CTMACDA). All these m combination of attributes valuesequally have high occurrence rate among k nearest trades toCBundlei.

Example 4, shows the need for an extension on mkNN in multi-attribute scenario.

Table 4Sample traded packages most similar to an optimal package h4 pairs of Shoes, 4 Bags,8 Shirts, 8 Trousers, 2000i in a 2-attribute combinatorial e-marketplace.

Package Price Payment

5 pairs of Shoes 3 Bags 10 Shirts 6 Trousers 2000 Credit4 pairs of Shoes 3 Bags 10 Shirts 6 Trousers 2050 Check4 pairs of Shoes 2 Bags 9 Shirts 8 Trousers 1900 Credit5 pairs of Shoes 3 Bags 10 Shirts 6 Trousers 2010 Credit5 pairs of Shoes 4 Bags 9 Shirts 5 Trousers 2000 Cash3 pairs of Shoes 4 Bags 10 Shirts 5 Trousers 1800 Check5 pairs of Shoes 2 Bags 8 Shirts 7 Trousers 1900 Check5 pairs of Shoes 4 Bags 10 Shirts 6 Trousers 2010 Credit4 pairs of Shoes 2 Bags 9 Shirts 5 Trousers 1995 Check

Example 4. Assume the same CBundlei of Example 3 is the optimalcombinatorial multi-unit bundle recommended to the bidder agenti in a 3-attribute combinatorial e-marketplace, where package-based attributes are Price, Payment Method, and Delivery. Amongall transactions in TMACDA, again suppose mkNN learning (withk ¼ 9) explores nine transactions shown in Table 5 as 9-nearestneighbors of CBundlei based on quantities of its items and thepackage price.

In determining appropriate values for package-based attributes ofthe instance, first suppose we do two separate mk-NNs for querying‘‘payment method’’ and ‘‘delivery’’. The first mk-NN suggests both‘‘Credit’’ and ‘‘Cash’’ (among ‘‘Credit’’, ‘‘Check’’, and ‘‘Cash’’) for pay-ment method (both with the majority of 4/9) and the second one intro-duces ‘‘1 Day’’ and ‘‘1 Week’’ (among ‘‘1 Day’’, ‘‘1 Week’’, ‘‘10 Days’’,and ‘‘1 Month’’) for delivery (both with the majority of 3/9). Therefore,all combinations hCredit, 1 Dayi, hCredit, 1 Weeki; hCheck, 1 Dayi,and hCheck, 1 Weeki seems to have the same ranks. However, weobserve that hCredit, 1 Weeki and hCredit,1 Dayi (both with themajority of 2/9) are two highly occurred ‘‘combinations’’ (i.e., multiplecombinations) of payment and delivery attribute values than hCheck,1 Dayi and hCheck, 1 Weeki (both with the majority of 1/9)11. Thatis, by these m ¼ 2 combination of attributes values recommendedby mkNN-Com learning, the bidder agent is now recommended with

MACPACKi ¼hh4 pairs of Shoes; 4 Bags; 8 Shirts; 8 Trousers; 2000i;fhCredit; 1 Dayi;hCredit; 1 Weekigi: �

4.6.3. A combinatorial multi-valued k-nearest neighbor learningalgorithm

Fig. 11 depicts multi-dimensional multi-valued k-nearestneighbor learning algorithm for determining major Combinationsof interdependent package-based attribute values. We call thismombinatorial mkNN learning algorithm mkNN-Com.

This algorithm first assign a distance to each confident transac-tion r in CTMACDA (see also Section 4.6.1). Euclidian distance iscomputed among CBundlei quantities of goods and its price withrespect to quantities of goods and price of each transaction (asshown in Distance(R, CBundle) in Fig. 11). CTMACDA transactionsare sorted based on their distance values in ascending order.

When only one attribute c is considered, assume n ¼ kQnC

c¼1nvc ,where nvc is the number of values of the package attribute and k isa constant determining number of neighbors. The algorithm firstplaces attribute values of (at most) top ntransactions of the sortedCTMACDA in TOPN. It then finds which attributes combination hasthe majority within TOPN attribute combinations. It is worth not-ing that only combinations that observed in TOPN are considered(than all possible combinations of attributes values). To do that,support of each attributes combination in TOPN is computed. Allm > 1 combinations with the highest rank of occurrence in TOPNare then recommended combination of package-based attributesfor CBundlei. When no confident transaction has been available inCTMACDA, the algorithm assigns the bundle’s attributes combina-tions of values with the highest support in TMACDA.

4.7. Bid generation module

This module is the last among three core modules in prescribinga multi-attribute combinatorial bid to a bidder. By this end, thebidder agent has generated MACPACK, a package of multi-attributesubstitute optimal combinatorial bundles. We call each of thesecandidate bundles a MACBUNDLE. In this module the bidder agentfirst sorts these MACBUNDLEs based on their utilities. Using the

11 In the worst case, the combination of attribute values may even consist of anattribute value which is not individually highly occurred.

Table 5Sample traded packages most similar to an optimal package h4 pairs of Shoes, 4 Bags, 8 Shirts, 8 Trousers, 2000i in a multi-attribute combinatorial e-marketplace.

Package Price Payment Delivery

5 pairs of Shoes 3 Bags 10 Shirts 6 Trousers 2000 Credit 1 Day4 pairs of Shoes 3 Bags 10 Shirts 6 Trousers 2050 Check 1 Day4 pairs of Shoes 2 Bags 9 Shirts 8 Trousers 1900 Credit 1 Week5 pairs of Shoes 3 Bags 10 Shirts 6 Trousers 2010 Credit 1 Week5 pairs of Shoes 4 Bags 9 Shirts 5 Trousers 2000 Cash 1 Month3 pairs of Shoes 4 Bags 10 Shirts 5 Trousers 1800 Check 1 Month5 pairs of Shoes 2 Bags 8 Shirts 7 Trousers 1900 Check 10 Days5 pairs of Shoes 4 Bags 10 Shirts 6 Trousers 2010 Credit 1 Day4 pairs of Shoes 2 Bags 9 Shirts 5 Trousers 1995 Check 1 Week

Fig. 11. Finding promising combinations of package attributes using combinatorial multi-valued k-nearest neighbor algorithm.

19 December 2014

bidder’s preferences, it then recommends the best MACBUNDLEsuite to the bidder’s preferences for proposing as MACBID to MAC-

DA. MACBID is devised from market trades data, the bidder’s Item-Set, and his/her preferences.

13151316

13181318

13381339

13411341

13711372

13741374

13851386

13881388

Table 6An ordered MACPACK.

Bundle Price Payment Delivery Utility

4 pairs of Shoes 4 Bags 8 Shirts 8 Trousers 2000 Credit 1 Day 1.004 pairs of Shoes 4 Bags 8 Shirts 8 Trousers 2000 Check 1 Day 0.904 pairs of Shoes 4 Bags 8 Shirts 8 Trousers 2000 Cash 1 Week 0.594 pairs of Shoes 4 Bags 8 Shirts 8 Trousers 2000 Check 1 Month 0.20

19 December 2014

4.7.1. Ranking MACBUNDLEsAll MACBUNDELs in MACPACK have the same return rate. How-

ever, they differ in their attribute values12. Top attribute values rec-ommended by the market may or may not be valuable for the agent ashe/she may value an attribute value worthless or unavailable. The bid-der agent then applies bidder’s valuations on the attributes for rankingmulti-attribute combinatorial bundles recommended in MACPACK byEq. (43). The agent assigns weighted multi-attribute utility value toeach MACBUNDLE as described in Section 4.3.1 and then sorts allMACBUNDLEs based on their utility values in descending order

OMACPACKi ¼ hhhquantityig : g

¼ 1; . . . ;Nii;pricei; hvwðc1Þ; . . . ;vwðcnC Þi;Utilityi

wi: w ¼ 1; . . . ;mii

ð44Þ

where, m is the number of MACBUNDLEs in MACPACK determinedusing mkNN-Com Learning in Section 4.6.2.

We explain the approach adapting Nassiri-Mofakham et al.(2008) and Nassiri-Mofakham et al. (2009b) in Example 5.

Example 5. Assume a 3-attribute e-marketplace where packagesare traded based on Price, Delivery, and Payment Method. SupposeDelivery includes five methods, namely: 1 Day, 2 Days, 1 Week,10 Days, and 1 Month. Payment Method denotes the three Cash,Credit, and Check methods. We suppose that the bidder agentscores all attributes to values between 0 and 100. Assume theagent weights Delivery and Payment Method to 0.7 and 0.3,respectively. Moreover, the bidder agent assigns the followingvalues to each Delivery and Payment Method:

Delivery value: 1 Day = 100, 2 Days = 70, 1 Week = 70, 10 Days= 40, 1 Month = 0

Payment Method values: Cash = 60, Credit = 100, Check = 80.Therefore, RVDelivery ¼ 0;AVDelivery ¼ 100, and RVPayment ¼ 40;

AVPayment ¼ 100.Now, assume that the recommended MACPACK to this bidder

agent is the following m ¼ 4 multi-attribute combinatorial bundles

MACPACKi ¼ h4 pairs of Shoes; 4 Bags; 8 Shirts; 8hTrousers; 2000i; hCredit; 1 Dayi; hCash; 1 Weeki;fCheck; 1 Monthi; hCheck; 1 Dayih gi:

The agent then assigns utilities to MACBUNDLEs using Eq. (1)and sorts them as shown in Table 6.

4.7.2. Devising MACBIDThis component, as the final component in the bidding agent

strategy, recommends him/her a single multi-attribute combinato-rial bid. Among the market- and preference-based multi-attributeoptimal bundles of multi-unit goods, the recommendation offersthe agent this bid based on his/her preferences (see Section 4.3).

Assuming the Ordered MACPACK in Eq. (44) and adapting theapproach presented by Nassiri-Mofakham et al. (2009b), we sup-pose BUi ¼ OMAKPACKiðmÞ:Utility and Bui ¼ OMAKPACKið1Þ:Utility

12 As shown in Eq. (43) each MACBUNDLE consist two parts: a combinatorial bundleof multi-unit goods and a combination of package-based attribute values.

are two attainable boundary utilities for a bidder agent i, wherem is the number of MACBUNDLEs in MACPACK determined usingmkNN-Com Learning Algorithm (see Section 4.6.2). We recom-mend the agent a single MACBUNDLE by a method similar to theapproach presented in personality-based bargaining model(Nassiri-Mofakham et al., 2009b).

In pricing, the seller and buyer agents’ desires for pricing are inopposite sides. However, in utility-based selection, their desiresare in the same direction. That is, the approach for considering util-ities of multi-attribute alternatives is the same for seller and buyeragents. Nonetheless, they have already may have set different eval-uations for the same attribute value. The approach presented byNassiri-Mofakham et al. (2009b) proposes the best initial offerbased on the risk factor of a buyer or seller agent. The approachemploys cooperation factor during negotiations, when agents arebeing informed of their counterpart offers. In MACDA, the agentsare already informed of market trades history. Therefore, weextend the mentioned approach by defining a new evaluation fac-tor EVi (0 6 EVi

6 1) as

EVi ¼ dðRi;1� CPi;aiÞ ð45Þ

where, d is defined as Eq. (11) and ai is described as Section 4.3.3. Itis also worth noting that Ri and CPi moves in opposite directions tomake the utility in an extremum value, while to find an optimalcombination of goods, Ri and CPi moves in the same direction foroptimizing risk and return of the combination (See also Sections4.3.3 and 4.5.3). Therefore, we employed 1� CPi (than CPi thatwas used for RLi factor in Eq. (12)) to define EVi factor.

The best MACBUNDLEiw 2 OMACPACKi

;w ¼ 1; . . . ;m (i.e.,MACBIDi) is then a MACBUNDLE at row w in OMACPACKi so thatOMAKPACKiðwÞ:Utility has the first utility value equal to or greaterthan utilityi where,

utilityi ¼ EViBUi þ ð1� EViÞBui: ð46Þ

Example 6 depicts the approach for generating MACBID pre-sented in Fig. 12.

Example 6. Suppose that several agents concluded in an OMAC-PACK presented in Table 6. In Table 7, we show the recommendedutility and then MACBID for each of nine (among all) stereotypicalagents. j

In most of the research for allocation in CAs, XOR-bid isemployed instead of a single MACBID. Therefore, a bidder may sub-mit devised MACPACK to an auction. Moreover, the agent mayexplores different optimal bundles (see Section 4.5.3) by changinghis/her a parameter and then submit XOR of MACBIDs constructedby those optimal bundles.

In the following section, we now present a Test Suite for evalu-ating MACBID strategy.

5. Evaluating MACBID strategy

MACBID generates meaningful bids based on the endowments,valuations, constraints and personality of the bidder as well asmarket data. Our objective is to model an automated bidding based

Fig. 12. Selecting MACBID.

Table 7MACBIDi s prescribed for nine seller agents recommended with the same OMAKPACKi .

i ¼ 1 Agent’s Ri ¼ 0, CPi ¼ 0:52, ai ¼ 1, EVi ¼ 0:24, Recommended utilityi ¼ 0:39

MACBIDi ¼ hh4 pairs of Shoes;4 Bags;8 Shirts;8 Trousers;2000i; hCash;1 Weekii Utility = 0.59

i ¼ 2 Agent’s Ri ¼ 0, CPi ¼ 1, ai ¼ 1, EVi ¼ 0, Recommended utilityi ¼ 0:20

i ¼ 3 Agent’s Ri ¼ 0:14, CPi ¼ 0:52, ai ¼ 0:46, EVi ¼ 0:25, Recommended utilityi ¼ 0:40

MACBIDi =hh 4 pairs of Shoes, 4 Bags, 8 Shirts, 8 Trousers, 2000i,h Cash,1 Weekii Utility=0.59

i ¼ 4 Agent’s Ri ¼ 0:52, CPi ¼ 0:24, ai ¼ 0, EVi ¼ 0:25, Recommended utilityi ¼ 0:62

i ¼ 5 Agent’s Ri ¼ 0:85, CPi ¼ 0:24, ai ¼ 0, EVi ¼ 0:85, Recommended utilityi ¼ 0:88

i ¼ 6 Agent’s Ri ¼ 1, CPi ¼ 0:24, ai ¼ 0:4, EVi ¼ 0:92, Recommended utilityi ¼ 0:94

MACBIDi ¼ hh4 pairs of Shoes;4 Bags;8 Shirts;8 Trousers;2000i; hCash;1 Weekii Utility = 1

i ¼ 7 Agent’s Ri ¼ 1, CPi ¼ 1, ai ¼ 0, EVi ¼ 1, Recommended utilityi ¼ 1

MACBIDi ¼ hh4 pairs of Shoes;4 Bags;8 Shirts;8 Trousers;2000i; hCash;1 Weekii Utility = 1

i ¼ 8 Agent’s Ri ¼ 1, CPi ¼ 1, ai ¼ 0:46, EVi ¼ 0:68, Recommended utilityi ¼ 0:75

i ¼ 9 Agent’s Ri ¼ 1, CPi ¼ 1, ai ¼ 1, EVi ¼ 0:50, Recommended utilityi ¼ 0:60

19 December 2014

on the above-mentioned parameters rather than prescribing thebest roles for the sellers or buyers. Therefore, the true evaluationof MACBID could be against human bidders to determine if MAC-BID correctly model the bidders’ decision-making.

Nonetheless, for evaluating the strategy we employ CATS-simi-lar data extended for multi-unit and multi-attributes markets.Although Combinatorial Auction Test Suite (Leyton-Brown et al.,2000; Leyton-Brown & Shoham, 2006) generates more realisticbids than distributions employed in previous studies in CAs, it doesnot model market realities such as multi-unit items and discountswhich is considered in MMUCA test suite (Vinyals et al., 2008).MMUCA although deals with the latter, it is a test suite designedfor specific mixed multi-unit combinatorial auctions where a pro-curement involves a mixture of forward and reverse combinatorialauctions.

We evaluate MACBID using MACDATS, a MACDA Test Suitewhich adapts required CATS and MMUCA features and more (e.g.,realistic limited discounts, package attributes, and buyer and sellerroles) for multi-attribute combinatorial double auction. MACDATSgenerates artificial but amenable data for trades history due to thesynergetic relationships among goods and discounts for items andattributes of packages traded in multi-unit and multi-attributescenario.

We benchmark MACBID by analyzing its efficiency againststate-of-the-art bidding strategies in CAs.

5.1. Benchmark strategies

As shown in Table 1, bestResponse, INT, and CATS-3 strategies aredesigned for a single-unit and single-attribute market. To be com-

14471448

14501450

14511452

14541454

14551456

14581458

14681468

14781478

14801481

14831483

14981498

14991500

15021502

15031504

15061506

15151516

15181518

15191520

15221522

15381539

15411541

15471548

15501550

15511552

15541554

19 December 2014

parable with MACBID, they are first extended for a multi-unitmulti-attribute scenario. This comparison is presented in Section5.3. We also note that these strategies consider only a self-inter-ested agent, while MACBID models different behaviors humanexhibit in a market.

5.1.1. Best response plus strategyThe bestResponse bid (Bichler et al., 2009; Parkes & Ungar, 2000;

Pikovsky, 2008) maximizes the bidder’s surplus if he or she were towin it at current prices. As a bidder agent trading in MACDA, bes-tResponse bidder needs to employ Market Processing Module (aspresented in MACBID, Section 4.4) to be informed of market priceslg of each good g 2 ItemSeti . The bidder agent determines themost profitable bundle S so that

S # ItemSeti; SurplusðSÞP SurplusðTÞ; 8T # ItemSeti

where,

SurplusðSÞ ¼Xg2S

SurplusðgÞ; SurplusðgÞ ¼ lg � RVig :

The agent then prices the bundle S as

priceðSÞ ¼Xg2S

Regarding Constraints 1–3, 4B and 4S, for extending bestResponse toa multi-unit scenario, two approaches are presented for seller andbuyer agents.

(a) The bestResponsePlus SellerThe BR seller agent greedily adds all goods with positive surplus

to the bundle. For these goods, he puts all available Q ig (see Eq. (6)

in Section 4.2.3) into the bundle and values S as

priceðSÞ ¼Xg2S

lgQ ig ; SurplusðgÞ ¼ lg � RVi

g > 0:

For each packaged-based attribute, he selects a value with the high-est utility according to the bidder’s valuation (see Section 4.2.3).

(b) The bestResponsePlus BuyerThe greedy BR buyer agent needs to consider her budget regard-

ing bundling and multi-unit goods. Among all goods with positivesurplus, she iteratively adds qi

g units of the most profitable goodg 2 ItemSeti, so that

SurplusðgÞ ¼ RVig � lg > 0 and qi

¼ min Max validgq;

available budgeti

where Max validgq is the maximum tradable quantities of good g in

the market. The price of the bundle S is then

priceðSÞ ¼Xg2S

lgqig :

For selecting attribute values, she acts similar to BRP seller agent.

5.1.2. INT Plus StrategySimilar to BRP strategy, the INT bidder (An et al., 2005; Bichler

et al., 2009; Pikovsky, 2008) also needs to find market prices lig

of each good g 2 ItemSeti using MACBID’s Market ProcessingModule.

(a) The INTP SellerAn INTP bidder agent considers a matrix of pair-wise synergy

values of goods and puts all available Qig ; g 2 ItemSeti, into the bun-

dleS, where it is a bundle with the highest average unit utilityvalue. That is, he enumerates all bundles of goods g 2 ItemSeti toexplore a bundle S with the highest v iðSÞ where,

v iðSÞ ¼Xg2S

Q igSurplusðgÞ þ 2

jSjXg2S

Xh2S;h–g

syniðg;hÞ

SurplusðgÞ ¼ lg � RVig :

The agent then set price of S as

priceðSÞ ¼Xg2S

lgQ ig :

Value of each package attribute is selected similar to the BRPstrategy.

(b) The INTPlus BuyerThe INT buyer agent similarly exploits a matrix of pair-wise

synergy values for determining the most synergetic goods. As sheneeds to consider her budget limit, she randomly generates N(e.g., 200 �jItemSetij) sample combinations of goods quantities qi

g .She then selects a combination S with the highest synergetic valuev iðSÞ, where for g 2 ItemSeti

SurplusðgÞ ¼ RVig � lg

priceðSÞ ¼Xg2S

lgqig :

For attribute values, she behaves similar to INTP seller agent.

5.1.3. CATS-3 Plus StrategyIn CATS-3 strategy (Leyton-Brown et al., 2000; Leyton-Brown &

Shoham, 2006), each agent knows the common value of each good.For that, the bidder agent in MACDA needs to employ MACBID’sMarket Processing Module in MACDA. The agent also uses goods’private values. To do that, we equip CATS3P bidder with MACBID’sUnitPricing component. Once the strategy generates the synergeticbundle, its price is determined using pricingi

g (which is determinedaccording to common value li

g and g’s private value). Selectinggood g 2 ItemSeti is according to a normalized matrix of pair-wisesynergy values of goods. For details of the strategy, please refer to(Leyton-Brown et al., 2000; Leyton-Brown & Shoham, 2006).

(a) The CATS3P SellerThe CATS3P seller then puts all available Qi

g of those goods intothe bundleSand prices the bundle as

priceðSÞ ¼Xg2S

pricingigQi

For each packaged-based attribute, he selects a value with the high-est utility according to the bidder’s valuation.

(b) The CATS3P BuyerOnce a high synergetic good is selected, the CATS3P buyer agent

also needs to consider to the bidder’s budget limit. She puts qig

quantities of this good g 2 ItemSeti where

qig ¼min Max validg

q;available budgeti

pricingig

and prices the bundle as

priceðSÞ ¼Xg2S

pricingigqi

For selecting attribute values, she acts similar to CATS3P selleragent.

16001601

16031603

16041605

16071607

16141615

16171617

19 December 2014

5.2. The MACDATS setup

The purpose of MACDA Test Suite is to generate market historyof trades as well as sampling goods, selling and buying bidders.MACDATS consists eight main routines for modeling primitiveassumptions for the market, sampling goods, sampling goods relation-ship, sampling trades attributes, sampling market trades history, sam-pling sellers, sampling buyers, and benchmarking MACBIDders.

5.2.1. Simulating the marketThe market is simulated through setting up market primitives

as well as trades history. We setup the market with nG ¼ 8goods each with Min validg

p ¼ Min validgq ¼ 1 and Max validg

p ¼Max validg

q ¼ 100. In addition to package’s price, there are nC ¼ 3packaged-based attributes, each with at most nvC ¼ 5 values.Goods are in synergetic relationship using a pairwise synergymatrix. The history of the market is setup by 1000 package trans-actions, where each package is generated by synergetic goodsusing a multi-unit CATS-similar good selection method. We alsoemploy a MMUCA-similar discounting method. However, to bediscounted, a minimum required and up to an upper limit of thegood’s quantity should be traded.

5.2.2. Simulating biddersFor evaluating MACBID, we test it using sampling sellers and

buyers who employ MACBID strategy against sellers and buyerswho bid under BRP, INTP, and CATS3P strategies. All bidders pro-pose their bids according to their own item set. That is, they bidonly for goods in their item set (stock/need) with respect to eithertype or quantity as well as trade attributes that they afford to con-sider. A bidder agent is now equipped with the following informa-tion: (1) a unique id + role (2) bidder’s risk factor, (2) bidder’scooperation factor, (3) bidder’s item set, (4) budget limit (if abuyer), (5) maximum available quantity of each good (if a seller),(6) attributes value set for the bidder, (7) pair-wise synergy matrixof goods, (8) the strategy id, and (9) predicted prices of goods in themarket.

In Section 5.3, we evaluate MACBID and multi-unit multi-attri-bute extensions on state-of-the-art bidding strategies in CAs (Sec-tion 5.1).

5.3. Evaluation and behavior of MACBID

We assign a bid two values: success rate and error rate. Winnerdetermination policy (see Section 3.2.3) considers Eq. (4) thatproposes an upper bound for a bid to be supposed as a candidate

Table 8First sample item set for selling.

Constraint Good 1 Good 2 Good 3 Good

43 20 8 19

71.0281 37.0375 26.5414 40.591

74.8269 44.1313 26.3501 39.069

13.1065 12.7597 9.7108 10.639

Table 9Second sample item set for selling.

49 20 0 23

77.5859 40.697 0 43.29

75.5624 40.4949 0 45.70

11.371 11.771 0 14.25

winner. This bound determines the bid’s success percentage. Thiscan be done by enumerating bids of other participants in the otherside of the market that may be satisfied with the bid. That is,

successðbidiÞ ¼ Avgtrader2VMACDA

distðbidi; traderÞ ð47Þ

where,

distðbidi;traderÞ¼max

ð�1ÞuðiÞ qig�qr

g8g 2G;

ð�1ÞuðiÞðpricer�priceiÞpricei

and uðiÞ is defined as Eq. (23). pricer and qrg are the package’s price

and quantities of goods g in bid r, respectively. Similarly, pricei andqi

g are respectively the package’s price and quantities of goods g inthe agent i’s bid.

Error rate of a bid is defined as the average number of attributesin transactions whose attributes values differ from those in the bid.That is,

aErrðbidiÞ ¼ Avgtrade r2VMACDA

� number of attributes c; v iðcÞ – v rðcÞnC

ð48Þ

where, template of bid r is matched with bidi and v iðcÞ and v rðcÞ arethe values of the package attribute c in bidi and bidr , respectively.

It is worth noting that success rate of a bundle is a numberbetween 0 and 1, while error rate of package attributes is describedas a percentage.

5.3.1. MACBID evaluationThe true evaluation of MACBID could be against human bidders

to compare if MACBID correctly model the bidders’ decision mak-ing. Nonetheless, in this section we show the measures for biddingunder MACBID and extended benchmark strategies. To do that, weendow item sets to bidders that we generated in Section 5.2.2. Twotwenty item sets are generated for selling and buying, respectively.Seller agents are simulated with reservation values and availablequantities of goods in the item sets, while buyer agents need toconsider their reservation values and budget limits.

To compare MACBID, BRP, INTP, and CATS3P per each item set,we generate different stereotypical behaviors through differentvalues for Ri and CPi per each strategy. With values of 0, 0.25,0.50, 0.75, and 1 for Ri and CPi, twenty-five behaviors are consid-ered for bidders using each strategy. We first compute RLi for eachagent using Eq. (11). Success rate of bundles and error rate of pack-

4 Good 5 Good 6 Good 7 Good 8

3 13 14 3

8 5.2859 17.5993 84.293 92.5985

22.0095 22.4322 79.875 83.4205

8 8.8197 9.8153 15.3006 9.9084

4 3 0 0

8 4.9123 17.5258 0 0

81 22.716 19.1341 0 0

98 8.4684 8.204 0 0

19 December 2014

age attributes of each bid are then computed through Eqs. (47) and(48).

Tables 8 and 9 show two different item sets endowed to twoseller agents. The last two rows of each table depict the valueand deviations of goods’ prices predicted by these seller agents.

Figs. 13 and 14 show that by increasing the rationality factor ofagents, success rate of MACBID stands higher than other strategies.It is the same for MACBID’s attributes, where its error rate is lowerthan of other strategies when the rationality of the agent isincreased. However, two greedy BRP and INTP strategies behavethe same for all agents in a success rate of 0.25.

Table 10First sample item set for buying with budget of 20,000.

0 39.2738 0 0

0 42.7654 0 0

0 12.2499 0 0

Table 11Second sample item set for buying with budget of 20,000.

83.7896 41.5405 25.6186 41.09

76.218 46.3351 33.4602 39.41

12.5476 15.4508 13.9747 10.58

Fig. 13. Evaluating bids for selling the first item set based on (a

Fig. 14. Evaluating bids for selling the second item set based on

Similarly, Tables 10 and 11 show two item sets of buying. Thebids proposed by four bidding strategies for these item sets aredepicted in Figs. 15 and 16, respectively. Again, it is observed thatsuccess rate of MACBID is increased by increasing the rationalityfactor of agents. It is the same for MACBID’s attributes, where itserror rate is almost decreased by increasing the degree ofrationality.

The average outcomes resulted from the four above mentionedstrategies for all twenty selling items sets and twenty buying itemsets each using 25 different behaviors for bidding agents are shownin Tables 12 and 13. It is observed that packages offered by both

4.7256 20.5308 89.6416 81.5678

25.5807 21.1419 79.0942 83.7905

11.2795 7.5031 13.9016 10.9978

7 5.1251 17.8069 84.7448 96.1352

58 23.3021 24.0088 78.83 80.5459

8 10.7967 10.067 14.8525 12.4094

) bundle’s success rate (b) error rate of package attributes.

(a) bundle’s success rate (b) error rate of package attributes.

Fig. 15. Evaluating bids for buying the first item set based on (a) bundle’s success rate (b) error rate of package attributes.

Fig. 16. Evaluating bids for buying the second item set based on (a) bundle’s success rate (b) error rate of package attributes.

19 December 2014

sellers and buyers using MACBID have the highest success proba-bility (0.38 for selling and 0.14 for buying). In addition, they ownthe lowest error percentage in valuation of package attributes(47% for selling and 46% for buying) with respect to benchmarkstrategies.

5.3.2. MACBID behaviorIn Section 5.3.1, we compared four strategies by aggregating all

bids based on the rationality factor of the agents. In this section, weanalyze the behavior of MACBID by considering risk and coopera-tion factor of the agents. We show the success probabilities of bun-dles and percentages of error in package attribute values through3D diagrams.

Table 13Average outcomes of four bidding strategies by twenty-five different buying agents.

Strategy MACBID

Average success probability of devised packages 0.14196Average error percentage of attributes’ values 45.6067

Table 12Average outcomes of four bidding strategies by twenty-five different selling agents.

Strategy MACBID

Average success probability of devised packages 0.378679Average error percentage of attributes’ values 46.82008

In Fig. 17, the highest success rate happens for an agent withRi ¼ 1 and CPi ¼ 0. For this item set (Table 8), agents withRi 2 ½0:75;1� and any CPi have proposed the most successful bids.In addition, when Ri 2 ½0:25;1� and CPi 2 ½0:25;1� the seller agentfaces with the least rate of error in attribute values of his bid.Therefore, the agents with the higher degrees of risks have moreconcentrations toward return of the packages (see Eq. (13)) andpropose bids that are more successful. Also, as shown in Fig. 18,the agents with Ri ¼ 0:75 and CPi 2 ½0:50;1� proposed bids withthe highest success probabilities, while the minimum rate of errorin attributes happens for the agents with Ri ¼ 1 and CPi ¼ 0:50. Forvalues Ri 2 ½0:75;1� and any CPi, we observe the least rate of errorfor attribute values. Again, this agent with high degrees of risk is asuccessful seller for trading the item set.

CATS3P INTP BRP

0.07984 0.113698 0.11110449.44674 47.36076 48.0008

CATS3P INTP BRP

0.201213 0.290233 0.29023349.05939 49.24563 49.24563

Fig. 19. The 3D representation of MACBID behavior for buy bids in Fig. 15 with respect to the agents’ risk and cooperation factors and based on (a) bundle’s success rate (b)error rate of package attributes.

42444648

0.050.10

0.150.20

Fig. 18. The 3D representation of MACBID behavior for sell bids in Fig. 14 with respect to the agents’ risk and cooperation factors and based on (a) bundle’s success rate (b)error rate of package attributes.

Fig. 17. The 3D representation of MACBID behavior for sell bids in Fig. 13 with respect to the agents’ risk and cooperation factors and based on (a) bundle’s success rate (b)error rate of package attributes.

19 December 2014

Please cite this article in press as: Nassiri-MofakhamQ1 , F., et al. Bidding strategy for agents in multi-attribute combinatorial double auction. Expert Systemswith Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.12.008

19 December 2014

For buying item set of Table 10, as shown in Fig. 19, agents withRi ¼ 0:50 and CPi 2 ½0;0:75� have the highest rates of success inbundling. The lowest rate of error in package attributes is observedfor agents with Ri 2 ½0:75;1� and any CPi. This lower rate happensfor Ri 2 ½0:50;0:75� and CPi 2 ½0;0:75�. These successful agents rep-resented negotiator behavior. In Fig. 20, a buyer agent with Ri = 1and CPi = 0 has faced with the highest rate of success in bundlingand minimum rate of error in package attributes. The agents havesuccessful bidding for Ri 2 ½0:75;1� and CPi 2 ½0;0:25�. For mini-mum rate of error in attribute values, the agents should avoid bid-ding with Ri 2 ½0;0:25� and CPi 2 ½0:75;1�.

5.4. Discussion and key findings

From Table 12, it is observed that the success probability ofpackages proposed by MACBID for selling is respectively 1.88,1.33, and 1.31 times more than those of CATS3P, INTP, and BRP.For package attributes, MACBID error is 0.954, 0.951, and 0.951times less than the errors by the above mentioned strategies,respectively. That is, the success probability of MACBID’ packageshave an average superiority 1.5 times higher than benchmarkstrategies, while their attributes’ errors are 0.952 times of errorsin these strategies.

Similarly, for packages proposed for buying, Table 13 showsthat the probability for MACBID with respect to CATS3P, INTP,and BRP is 1.78, 1.25, and 1.28, respectively. MACBID’s error inattributes’ values is 0.92, 0.96, and 0.95 with respect to CATS3P,

Fig. 21. Bundle’s success rate for MACBID sell bids with res

Fig. 20. The 3D representation of MACBID behavior for buy bids in Fig. 16 with respect terror rate of package attributes.

INTP, and BRP, respectively. That is, in average, the package pro-posed by MACBID has less error in valuation of attributes (0.94)and higher success probability (1.44) with respect to currentstrategies.

In addition, success probability of MACBIDs proposed by agentsthat are more rational is 1.37 and 1.05 times higher than bids ofagents with RLi < 0:5 for sellers and buyers, respectively. Agentsthat are more rational face with less error percentages that are0.99 and 0.98 times less than bids of packages proposed by lessrational agents for sellers and buyers, respectively.

Similarly, we consider the average success probability of pack-ages and average error percentages of attribute values devised byMACBID with respect to risk and cooperation factors (Section5.3.2) for two twenty different selling and buying item sets usingtwenty-five different behaviors for bidding agents. Fig. 21 showsthat increasing both risk and cooperation enhances the successprobability of packages proposed by sellers. As Fig. 22 shows, lessrisk or average cooperation both increases error percentages inattribute values for their packages.

With respect to nine different behaviors related to combinationof three fuzzy values low (L), medium (M), and high (H) for risk andcooperation factor of an agent (see Table 6 in (Nassiri-Mofakhamet al., 2009b)), we evaluate packages regarding the seller and buyeragents’ behaviors. Fig. 23 shows that raising the seller’s riskincreases his proposed package’s success probability and decreasesits error percentages. For each risk value, cooperation factor has apositive effect on the success probability of proposed packages. The

pect to the agents’ (a) risk and (b) cooperation factors.

o the agents’ risk and cooperation factors and based on (a) bundle’s success rate (b)

Fig. 25. Error rate of package attributes for MACBID buy bids with respect to the agents’ (a) risk and (b) cooperation factors.

Fig. 24. Bundle’s success rate for MACBID buy bids with respect to the agents’ (a) risk and (b) cooperation factors.

Fig. 23. Depicting (a) bundle’s success rate (b) error rate of package attributes of sell bids based on the MACBID agents’ behavior.

Fig. 22. Error rate of package attributes for MACBID sell bids with respect to the agents’ (a) risk and (b) cooperation factors.

19 December 2014

Please cite this article in press as: Nassiri-MofakhamQ1 , F., et al. Bidding strategy for agents in multi-attribute combinatorial double auction. Expert Systemswith Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.12.008

Fig. 26. Depicting (a) bundle’s success rate (b) error rate of package attributes of buy bids based on the MACBID agents’ behavior.

19 December 2014

figure describes that aggressive sellers have proposed the mostsuccessful package bids.

Similarly, we show the average of success probability and errorpercentages in buy bids proposed by MACBID buyer agents in Figs.24 and 25.

It is observed that buyer agents with medium degrees of coop-eration enjoy higher success probabilities and less error percent-ages in attribute values for their proposed packages. Medium andhigh risk values have respectively the same effects on increasingthe success probability and decreasing error percentages in attri-bute values of the packages proposed by buyers. Fig. 26 depictsalso depict that negotiator buyer agents (medium risk and mediumcooperation) have proposed the most success full packages.

6. Conclusions and future works

In this paper, we presented a novel strategy, MACBID, for bid-ding agents in a complex multi-attribute combinatorial doubleauction (MACDA). MACBID consists of two perception and biddinglayers and are implemented in six modules. These modules modelthe market and the bidder, process the market, bundle comple-ment multi-unit goods, package multi-attribute bundles, andfinally propose the best tailored bid for the bidder.

We also presented a novel model for pricing goods and bun-dling in a multi-good e-marketplace. We considered seller andbuyer roles, individual item set, valuations, personality-based fea-tures of the bidders and market data in pricing and bundling mod-els. The simulation results show that average success probability ofsell bids and buy bids using MACBID packages are about 50 percenthigher and average error for attribute values was 5 percent lowerthan existing strategies.

MACBID strategy could be adopted and adapted as an auto-mated bidder or a bidding support system in any problem in com-binatorial markets with double side and multi-attribute and multi-unit combinatorial demands and supplies proposed or inspired byhuman beings. In addition to only profit-maximizer agents whichare often considered in the literature, MACBID could well modeldifferent realistic human-like degrees of risk and cooperation atti-tudes related to the personality of the bidders and dynamic behav-ior of the market towards combinations of items. Section 6.1 givesmore details on the theoretical contributions and practical implica-tions of the paper. Future works are presented in Section 6.3.

6.1. Implications for theory

While the existing studies in auctions address truth-telling asthe dominant strategy for the agents, it is not clear what the truevaluation of each agent could be. By extending Markowitz ModernPortfolio Theory, the study proposed an algorithm for bidders topredict unit price of each good by observing just traded bundles

in the history of the market where each traded package revealsno information regarding individual item prices but the packageprice. Although all the bidders sense the same market information,using the proposed pricing algorithm (Fig. 7) each bidder finds howmuch an item is worth to him/her based on the predicted unitprices (Fig. 5) and associated risks from the market, the bidder’swish list (to buy or sell) as well as his/her cooperation and risk fac-tor (adapted from the Five Factor Model of Personality). This causestwo different agents who have the same item list could be simu-lated to assume different item prices and in turn bundle differentquantities of items and with different total bundle prices. In addi-tion, mkNN-Com algorithm (Fig. 11) finds the most appropriatepackage attribute values based on top m values used for tradingtop k bundles similar to the packaged items in the history of themarket. Finally, each bidder again can choose a package (MACBID,Fig. 12) different from those proposed by the other agents based ondifferent utilities they assign based on their risks and cooperationfactors. This helps the research on WDP to use more meaningfulbids than the bids generated using random distribution functions.

Briefly speaking, the main contribution of this paper is a novelbidding strategy for agents in a multi-attribute combinatorial dou-ble auction and summarized as follows:

� We proposed an extension to Markowitz Modern Portfolio The-ory and Five Factor Model of Personality for a personality-basedmulti-attribute combinatorial bid.� Adapting mkNN, multi-attribute substitutes of the devised bun-

dle of complementary goods were packaged. The FFM of person-ality and MAUT were employed for selecting MACBID amongsubstitute bundles in the package.� We extended MPT by introducing a personality-based objective

function and transformed price-based transactions to return-based transactions. For this transformation, we first predictedprices of individual goods in transactions; modeled agent’s pric-ing based on the role, item set and personality of the bidder;and then formalized the agent’s return.� A test suite provided algorithms for generating stereotypical

artificial market data as well as personality, preferences anditem sets of the bidders.

6.2. Implications for practice

The study has important implications in growing practice inapplications of combinatorial auctions, double auctions, and com-binatorial double auctions in different fields. In addition to the sce-narios similar to those employed in the paper, the practicalimplications of the study could be in existing and upcoming com-plex applications in multi-commodities industries that need pro-posing or requesting dynamic and personalized services. Stockexchange (Antweiler, 2014; Ausubel, Cramton, & Jones, 2014;

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Keiser & Burns, 2014), grid and cloud computing (Chang, Lu, Huang,Lin, & Tzang, 2013; Ding, Kang, & Liu, 2013; Lee, Wang, & Niyato,2013; Samimi, Teimouri, & Mukhtar, 2014), cognitive radio, TVlicenses and spectrum auctions (Martin Bichler, Shabalin, & Wolf,2013; Dong, Rallapalli, Qiu, Ramakrishnan, & Zhang, 2014; Zhonget al., 2013; Zhu, Li, & Li, 2013), logistics and transportation (Robu,Noot, La Poutré, & Van Schijndel, 2011; Satunin & Babkin, 2014;Triki et al., 2014; Xu & Huang, 2013), electricity and energy markets(Brandt, Wagner, & Neumann, 2012; Poudineh & Jamasb, 2014;Weidlich et al., 2012; Yang & Yao, 2014) and so on are the domainsin which MACBID and its components could be employed to sup-port both users and service providers in better decision-makingand efficient bidding in the complicated markets.

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6.3. Further research

In this study, we assumed packages are multi-attribute but thegoods are determined by only quantity and price. For futureresearch, MACBID could be extended for multi-attribute goods.Moreover, for predicting the value of each unit item from the indi-vidual price of the bundles of multi-unit items traded before in themarket, we assumed that the price of each traded item in the pack-age should have a meaningful deviation from the quasi-equilib-rium price of each item in the market (Section 4.4.2). Anotherstudy can solve this prediction problem by violating this assump-tion. In addition, a full implementation of MACDA mechanism isan important subject for further development of the research onbidding strategies in MACDA as it helps to evaluate bids under amechanism. By assuming the static behavioral parameters of bid-ding agent in single-shot MACDA, still another study could extendthe research by proposing adaptive bidding in a multi-round orcontinuous MACDA and learning as well as modeling emotionsaffected from MACDA feedbacks on the previous bids of the agentand its peers or counterparts.

We defined a concentration factor a ¼ 0:5 (see Section 4.3.3) asa static parameter affecting the agent’s objectives for trading offbetween risk and return of a bundle. However, a could be a staticor dynamic parameter depending on seasonal, cultural, continen-tal, or international situations. Modeling a in a multi-nationalMACDA could be the subject of another research.

By considering ontological concepts for describing relationshipsamong goods’ attributes, a study could propose another represen-tation for bidder’s preferences and bid generation.

Finally, the models for price predictions, pricing, bundling, andpackaging issues presented in this paper could be open and unfoldinteresting theoretical and practical space for a stream of furtherworks.

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