Auctions with Resale Opportunities: An Experimental

Study∗

Chintamani Jog†and Georgia Kosmopoulou‡

April 3, 2014

Abstract

We study first price asymmetric private value auctions with resale opportunities

presented in seller’s and buyer’s markets. We offer experimental evidence on bidding

behavior, prices and resource allocation. Building upon the Hafalir and Krishna

(2008) model, we find that bidders will bid higher in an auction if the resale market is

a seller’s market than a buyer’s market. There is a price/revenue-efficiency trade-off

established theoretically between these two resale regimes. In equilibrium, however,

final efficiency is high irrespective of the resale market structure. Evidence of bid

symmetrization and higher final efficiency is found in the buyer-advantaged resale

case.

JEL Classification: D44, C92

Keywords: Auctions, Resale, Experiments.

∗The authors would like to thank the Office of the Vice President for Research at the University of

Oklahoma for financial support. Any opinion, findings, and conclusions or recommendations expressed

in this material are those of the authors and do not necessarily reflect the views of the National Science

Foundation.†University of Central Oklahoma, 100 N. University Drive, Edmond, OK 73013; email: cjog@uco.edu‡National Science Foundation, 4201 Wilson Blvd, Arlington, VA 22230 and Department of Economics,

University of Oklahoma, 308 Cate Center Drive, Norman, OK 73019; email: georgiak@ou.edu

1

1 Introduction

Standard results in auction theory presume mostly the absence of resale options. How-

ever, the sale prices of government owned assets or public resources are often determined

by resale opportunities. Examples include spectrum license auctions and the ensuing sale

of telecommunication companies in the last decade, real estate sales, and more recently

the sales of rights to emit pollutants, especially greenhouse gases in established Emis-

sion Trading Schemes (ETSs or cap and trade schemes). The applicability of a market

framework with resale as a foreseeable option extends to (re)allocation of common pool

or common property resources which include fisheries, wildlife preserves and surface

water resources (White [22]).

When bidders are offered an option to resell in a secondary market they adjust their

bids in the primary auction market. Adding a resale opportunity introduces a common

value element to an otherwise private value auction (Haile [9]). If the winner of an

auction has all the bargaining power in the resale market (in what we call a seller-

advantaged resale regime), there will be a speculative interest in acquiring the item at

the auction stage knowing there is a chance to resell it (Hafalir and Krishna [7]). On the

other hand, if the loser of the auction has all the bargaining power in the resale market

(in a buyer-advantaged resale regime), such an interest is limited and the common value

at the auction stage is restricted. Thus we would expect more aggressive bidding and

higher resale prices in a seller-advantaged resale regime. In both cases, the common value

created by the resale opportunity would lead to a symmetrization of bids; in equilibrium,

bidders should behave as if they compete in a symmetric auction for a common value

whose size is determined by the structure of the resale market.

In the present work, we explore the impact of the resale market structure on bids,

linking them to efficiency and auction revenue. We use controlled experiments that

mimic the theory to study first price auctions with asymmetric bidders that have resale

opportunities. We find higher bids on average in a seller-advantaged resale regime than

in a buyer-advantaged resale regime. Interim efficiency, measured in terms of the pro-

portion of efficient outcomes realized at the conclusion of the auction stage, is the same

across regimes but higher in magnitude than predicted. Final efficiency is high irrespec-

tive of the structure of the secondary market. In the seller-advantaged resale regime, we

find statistically significant differences in the bid distributions, consistent with other ex-

2

perimental work (see Georganas and Kagel [4]). In the buyer-advantaged resale regime,

we provide some evidence in support of bid symmetrization; in highly asymmetric en-

vironments, however, conforming to the equilibrium strategy may generate undesirable

risks for those with values in the upper quartiles of the support.

Our motivation stems from our interest in studying and predicting the effectiveness

of Emission Trading Schemes. ETSs are seen as a successful market based approach

to handle the issue of pollutants and their ill-effects including climate change. The

structure of the secondary market for permits can have a significant effect on bidding

behavior, initial and final allocative efficiency in ETSs. A sizable portion of the emission

allowance futures and option contract trades are carried out via the over the counter

(OTC) exchange through bilateral negotiations.1 Under these circumstances, one can

expect firms on either side to exploit bargaining power. The secondary market for Re-

gional Greenhouse Gas Initiative (RGGI) allowances, for example, was a buyer’s market

(indicated by low prices and volume of trading) until very recently, when prices started

to rise and brought about a reversal in the trend. In the near future, more stringent

caps may generate higher demand in the secondary market, thereby shifting the bar-

gaining power more from buyers to sellers. The California Cap-and-Trade program was

launched in November 2012 as the second largest emission trading market in the world

right behind the European Union Emissions Trading Scheme (EUETS). It attempts to

regulate emissions via reducing the cap by 2-3% a year leading to a projected reduction

from 522MT/person/year in 2010 to 85MT/person/year in 2050.2,3 The stringent caps

are likely to shift market power from buyers to sellers. The questions we ask are: How

will prices and efficiency be impacted from such a shift? Since we do not have the ability

to link directly bids in the primary and secondary markets for emission permits, neither

1Market Monitor Report, Regional Greenhouse Gas Initiative, 2010.2The urgency to step up efforts to meet carbon reduction goals was underlined in the 2010 World

Bank report that has been revisited by the news media after hurricane Sandy hit the east coast (see theWashington Post article by Howard Schneider, November 19, 2012.)

3At the international level, in the climate change conference of 2011, held in Durban, South Africa,the countries of the EU and a number of other developed countries have signed up to a second commit-ment period of the Kyoto Protocol, that ends in 2013. This will ensure that there is still some form oflegally binding treaty in place to cut carbon emission before the new agreement made by 190 partici-pating countries including the US, China and India takes effect at the end of 2020 (Gray [23]). Therehave been speculations about possible market concentrations in the event of international cap and tradesystem will be developing down the line. It is suggested that the US will be a dominant buyer and thecountries from Former Soviet Bloc would be dominant suppliers of pollution permits under Annex I ofKyoto protocol (Nordhaus and Boyer [20]). This might give enormous leverage to the supplier countriesto exercise their market power and drive up allowance prices.

3

do we have direct knowledge of firm expectations at the time of bidding, what can we

learn from our experimental subjects? Is bidding behavior conforming to the theory? Is

final efficiency as high as predicted by the model?

The paper is structured as follows. The next subsection reviews related literature.

Section 2 presents the theoretical framework followed by equilibrium bid and (ex-ante)

efficiency predictions. Section 3 describes the experimental design. Section 4 presents

the main results and related discussion. The final section offers concluding remarks.

1.1 Related Literature

Cox et al.[2] introduced the notion of a resale opportunity as an expository device to

explain value generation to experimental subjects. They postulate that values are gen-

erated out of idiosyncratic resale opportunities where the winning bidder could resale

the object to the auctioneer for a predetermined monetary value. The recent literature

discussed below links resale opportunities to the existence of a secondary market among

auction participants introducing a common value component to auction competition.

Haile’s [9] theoretical paper is among the earliest to analyze auctions with resale

as a two stage game. Using the first price, second price and English auction settings,

he shows that valuations are determined endogenously when forward looking bidders

take into account the possibility of resale in a secondary market. Hence, the revenue at

the auction stage depends on the resale market structure and the information linkage

between primary and secondary markets. He tests empirically this result in [10] using

data on U.S. Forest Service timber sales. Haile [11] extends the theoretical research by

constructing a two stage game, using three auction formats (first price, second price and

English auctions) in the first stage and two auction formats (optimal and English) in

the second stage. He focuses on the effect of the resale market on equilibrium bidding

strategies.

More recently, Hafalir and Krishna [7, 8] and Cheng and Tan [1] have studied revenue

generation and market efficiency in independent private value (IPV) auctions with resale.

These papers consider two types of bidders with asymmetric value distributions. Hafalir

and Krishna focused on the revenue ranking between first and second price auctions with

resale. One of the major insights from this work is the symmetrization property. Given

the resale market structure, for every first price asymmetric auction with resale, there is

an equivalent first price symmetric auction without resale. Asymmetric bidders behave

4

as if they are competing in a symmetric auction for a common surplus determined by the

nature of resale competition. In equilibrium, their bidding distributions are the same for

those two auctions. We show theoretically that bid-equivalence between types should

hold in the buyer-advantaged resale case due to symmetrization and provide a quantile

regression analysis that permits testing across the distribution of values.

On the experimental front, there have been very few related studies. Mueller and

Mestelman [20] report experimental evidence on revenue and efficiency effects under

the monopoly/monopsony ( seller/buyer-advantaged) structures using a double auction

setting. In their experiments, the subjects are assigned the tradable coupons before the

double auctions begin. Hence, their setting effectively has only one stage.

Lange et al. [16] build upon Haile [9] and provide experimental support for the result

that bids are higher in auctions with resale than those without, emphasizing the common

value element. Their setup is a two stage game with the second stage market structured

in some experiments as an English Auction and in others as an Optimal Auction. Players

decide on the bids only during the first stage. The second stage allocation is automated

and hence, players do not make any decisions at this stage.

Georganas and Kagel’s [5] study is the closest to ours. Their study also builds upon

Hafalir and Krishna [7] but their focus is on a comparison of bidding behavior across

resale and no resale scenarios. The resale scenario is the seller-advantaged resale regime.

Our paper compares the trade-off between revenue and efficiency across auctions with

seller-advantaged and buyer-advantaged resale. This is the first experimental test of

such a revenue-efficiency trade-off and could shed light on the continuing debate about

the optimal way to allocate emission permits.

More recently, Georganas [4] and Jabs-Saral [12] have studied English auctions with

resale using experiments. While Georganas [3] employs Quantal Response Function

(QRE) analysis to explain the signaling in English auctions with resale, Jabs-Saral’s

[12] focus is on the demand reduction and speculation following the shift of bargaining

power from buyer to seller in the resale stage. Unlike Jabs-Saral’s work, our paper uses

an asymmetric value structure and explores the impact of the form and characteristics

of the secondary market on efficiency.

We study a two-stage model, consisting of an initial first price auction followed by a

resale stage structured either as a seller or a buyer-advantaged market. The theoretical

framework is built upon the model by Hafalir and Krishna [7]. First, we solve explicitly

5

for equilibrium bidding strategies in the buyer-advantaged resale regime and provide a

comparison to corresponding strategies under seller-advantaged resale. Then, we perform

experiments and compare observed patterns of behavior to theoretical predictions.

2 Theoretical Framework

Two risk-neutral bidders are participating in a first-price independent private value

sealed bid auction. After the conclusion of the auction the winner has the opportunity to

participate in a seller-advantaged (buyer-advantaged) resale market. The winner (loser)

of the first stage auction can make a take-it-or-leave-it offer to sell (buy) the object to

(from) the same opponent. Both bidders’ values are drawn from independent uniform

distributions with different supports. The weak bidder’s value is an independent and

identically distributed (iid) draw from U[0, aw] wherein aw is set at 10 in all experimental

sessions that follow. The strong bidder’s value is an iid draw from U[0, as] wherein as

takes on the values 20 and 40 in two treatments of the experiment. We refer to the

former treatment as S20 and the latter as S40.

Bidding distributions and the type of resale regime are common knowledge among

the players. Players only know their own values and their own bids during the course of

the game. They do not learn the private values or bids of their opponents.

Consider first the auction followed by a seller-advantaged resale market. This implies

that the winner of the first auction has all the bargaining power in the secondary market.

Initially, we state the problem in general terms using F (.) as the cumulative density

function.

The problem for a bidder j winning the primary auction with a bid b is to determine

an optimal price p that maximizes the revenue function Rj

maxpRj = [Fi(φi(b))− Fi(p)]p+ Fi(p)vj

where φ is the inverse bidding function. The first term is the expected payoff from selling

in the second stage. The term in the bracket is the probability that the price is less than

or equal to the opponent’s value. The second term in this expression is the expected

payoff of bidder i when the price exceeds the opponent’s value and there is no trade.

Consequently, the problem for bidder j choosing the optimal bid in the primary

6

auction market can be stated as

maxb

Πj = Rj(p, b)− Fi(φi(b))b

where the first term is the expected revenue from the resale stage and the second term

is the cost to bidder j.

Similarly, consider the auction followed by a resale market with buyer-advantage.

The loser of the first auction has all the bargaining power in the secondary market. The

problem for bidder j losing the primary auction with a bid b is to determine an optimal

price r that maximizes the following resale profit Sj

maxrSj = [Fi(r)− Fi(φi(b))](vj − r).

The term in brackets is the probability of trade, which is determined by the resale

price being greater than or equal to the opponent’s value. Hence, Sj(r, b) represents the

maximum expected revenue received from the resale stage by bidder j.

The problem for bidder j choosing the optimal bid in the primary auction market is

then

maxb

Πj = Fi(φi(b))(vj − b) + Sj(r, b)

where Fi(φi(b)) is the probability of winning in the first stage.

The equilibrium bidding functions for each regime under the assumption of uniform

distribution of values are described in Table 1 where again, as and aw are the upper

bounds of the strong and weak bidder’s support respectively and vi is the value for

individual bidder i. The bid functions for the seller-advantaged resale regime follow

directly from Hafalir and Krishna [6] using the symmetrization property. The results

under the buyer-advantaged resale are derived along the same lines but require some

elucidation.4 The weak bidder’s value distribution sets an upper bound for the pricing

distribution in the secondary market. The highest price offered by the strong bidder

in the resale market should not exceed the upper bound of the weak bidder’s value

distribution. The equilibrium bid function for the buyer-advantaged resale is defined over

two intervals. For the first part, it is exactly the same as that in the seller-advantaged

resale regime. However, note that the bid and the resale price can never exceed the weak

4Refer to the appendix for a complete derivation.

7

bidder’s highest value. Hence for bids greater than aw2 , the optimal price is merely aw.

Once the resale price bound is known, we can derive equilibrium bidding strategies for

each player. The bidding functions are monotonic, continuous and increasing.

Table 1: Equilibrium Bidding and Resale Price Functions

Seller-Advantaged Resale Buyer-Advantaged Resale

Strong Bidder as + aw4asvs

as + aw4as

vs ∀ 0 ≤ vs ≤ 2awasaw + as

aw −asa

2w

vs(as + aw)∀ 2awasaw + as ≤ vs ≤ as

Weak Bidder as + aw4awvw

as + aw4aw

vw ∀ 0 ≤ vw ≤2a2w

aw + as

aw −a3w

vw(as + aw)∀ 2a

2w

aw + as≤ vw ≤ aw

Resale Price as + aw2awvw

as + aw2as

vs ∀ 0 ≤ vs ≤ 2awasaw + as

aw ∀ 2awasaw + as ≤ vs ≤ as

The optimal price in each regime depends on the inverse bidding functions φi(b) and

φj(b). The price function is p = 2b in the seller-advantaged resale regime. Under the

buyer-advantaged resale regime, the price function is r = 2b for bids less than or equal

to aw2 and r = aw for bids exceedingaw2 . In our setup, resale happens invariably from

weak to strong bidders. Note that, the weak bidder’s value distribution stochastically

dominates the resale price distribution under the buyer-advantaged resale regime. On

the other hand, the resale price distribution under the seller-advantaged resale regime

lies halfway between the strong and weak bidder’s value distributions.

Under the seller-advantaged resale regime, the speculative motive leads to higher

resale prices causing the weak types to bid higher at the auction stage. Weak bidders

who can successfully resell the good capture a larger surplus. However, the cost of

quoting higher final prices is the increased likelihood of overestimating the (strong)

opponent’s value and hence, higher final inefficiency. On the other hand, there is lack of

any significant speculative motive under the buyer-advantaged resale. This, along with

the resale structure that gives all bargaining power to strong bidder translates the upper

limit of the weak bidder’s support (aw) to an inevitable upper bound for the resale price.

Since the weak type never bids higher than aw under the buyer-advantaged resale, an

offer of aw from the strong type will always be accepted, leading to higher final efficiency.

8

This model leads to the following market behavior arising from the equilibrium con-

ditions:

Proposition 1: For any asymmetry between the bidders’ value supports, the equi-

librium average bids and resale prices under the seller-advantaged resale regime are

higher than those under the buyer-advantaged resale regime.

Proof: See the appendix.

Note that, the equilibrium bids for weak and strong type bidders are in proportion

to the ratio of their value distribution. i.e. for a given value, the weak bidder bids twice

as much as the strong bidder in the S20 treatment and four times as much in the S40

treatment under both regimes. This pattern arises as a consequence of the equivalence

of bidding strategies between two distinct games leading to the following property.

Symmetrization property: The bid distributions for weak and strong bidders are

identical within each regime.

Finally, the following proposition provides an efficiency comparison across regimes.

Proposition 2: Interim efficiency is identical under both the seller and buyer-

advantaged resale regimes. Higher predicted resale prices under the seller-advantaged

resale regime lead to lower final efficiency.

Proof: See the appendix.

Despite the price-efficiency trade off established here, the level of final efficiency remains

high across regimes.

3 Experimental Design

Our experimental design incorporates the details of this theory. We have two types of

bidders and two resale regimes. Since our focus is on understanding bidding behavior

across resale regimes, we kept the player types constant throughout the course of a

session. Instructions were distributed to subjects at the beginning of each session. There

were 40 rounds in each session divided equally between the seller-advantaged and the

buyer-advantaged resale regimes. The software was developed using z-Tree (Fishbacher

[3]).

Players received 65 ruchmas (our experimental currency) as the show up fee that

was used as initial capital in the S20 treatment. For the S40 treatment, players received

100 ruchmas to account for a larger disparity in the value distributions of bidders. The

9

conversion rate was 1$ = 13 ruchmas. At the beginning of every session, instructions

were read to the players accompanied by a Power Point presentation.5

There were two practice rounds followed by twenty rounds played for cash under each

regime. Valuations were drawn randomly for each round. The players were reminded of

their types at the beginning of each round. Each player was matched with an opponent

of the other type, and the matching was changed randomly from one round to another.

The information revealed was in line with the theoretical model. Each player knew his

own type and own private value. At the end of the auction, each player was informed

whether he won or not. In the second stage that followed immediately, the winning

(losing) player had an opportunity to make a take-it-or-leave-it offer to sell (buy) to

(from) the same opponent under the seller (buyer) advantaged resale treatment. If the

player did not want to sell (buy), he was advised to quote a price of 9999 (0) ruchmas.

Each round concluded with the final payoff displayed to each player depending on the

outcome. The resale rules and players’ value distributions were common knowledge. We

did not provide the players with a history of their bidding or earlier prices, since we

wanted them to treat each round independently as much as possible. The instructions

emphasized that each draw of value was separate. After two practice rounds (periods)

and twenty paid rounds of seller-advantaged resale treatment, players were informed

about the change in resale treatment. This was followed by another two practice rounds

and twenty paid rounds of the buyer-advantaged resale treatment. A brief questionnaire

followed that asked the players about some demographic information related to their

major, previous experience participating in auctions, risk preferences and gender.6 The

player’s ending balance was shown on the screen at the end of the questionnaire. This

concluded a typical session. Players received their earnings in Sooner Sense credit on

their university identity cards, which could be used for purchases around campus. The

players were recruited from the undergraduate and graduate student population at the

University of Oklahoma, Norman campus. For the S20 treatment, the number of subjects

per session varied from 4 to 12 with a total of 68 participants. For the S40 treatment, the

number of subjects per session ranged between 6 and 12 with a total of 54 participants.

5The instructions are attached at the end and presentation is available upon request.6For instance, a question on previous experience read as: “Have you previously participated in

real-life auctions? Please click yes or no.”

10

4 Results And Discussion

4.1 Descriptive Statistics

In Table 2, we show some of the descriptive statistics from the S20 and S40 treatments.

As seen from the table, the average bids and standard deviations are higher under the

seller-advantaged resale regime than under the buyer-advantaged resale regime. While

bidding in rounds 11-20 is isolated to examine more experienced bidders, the qualitative

Table 2: Average Auction Bids by Type, Treatment and Value Blocks

Player Type Value Block Seller Advantage Buyer AdvantageS20 Treatment

Rounds All 11-20 All 11-20

Weak

0 - 3.342.60 2.48 2.31 2.32

(2.79) (2.20) (2.12) (2.10)

3.34 - 6.675.18 5.18 4.68 4.66

(1.94) (1.93) (1.61) (1.32)

6.67 - 107.48 7.45 7.04 7.06

(2.00) (2.00) (1.56) (1.37)

Strong

0 - 6.672.70 2.66 2.55 2.43

(1.78) (1.74) (1.62) (1.58)

6.67 - 13.346.76 6.62 6.14 5.91

(2.19) (2.24) (1.83) (1.92)

13.34 - 209.53 9.37 7.78 7.47

(3.20) (3.06) (2.61) (2.48)S40 Treatment

Weak

0 - 44.14 2.52 2.04 1.98

(4.70) (2.41) (1.90) (1.78)

4 - 76.85 6.12 4.78 4.72

(4.71) (3.52) (1.60) (1.23)

7 - 109.53 8.99 7.48 7.30

(5.94) (5.63) (2.97) (1.85)

Strong

0 - 165.20 5.26 4.45 4.28

(3.94) (3.41) (3.11) (3.04)

16 - 2811.26 10.78 8.95 8.62(5.72) (5.33) (4.19) (4.16)

28 - 4016.81 14.37 12.03 11.78(9.99) (9.07) (7.11) (6.70)

Standard deviations are in parentheses.

11

results remain the same across.7,8

We also provide a non-parametric test to compare bid distributions across regimes

to test findings in Proposition 1. We employ the Mann-Whitney test under the null

of equality of bid distributions for the two regimes to test for difference in the location

across the two samples. For both treatments, we reject the null at p < 0.05 (S20: p-

value = 0.0065 and S40: p-value = 0.0374). Given the results of this test, the prediction

that average bids are higher under the seller-advantaged resale regime than the buyer-

advantaged resale regime is borne out.

05

1015

20

0 4 8 12 16 20

05

1015

20

Seller Advantage:Strong

Values

Bid

s

05

1015

20

0 4 8 12 16 20

05

1015

20

Buyer Advantage: Strong

Values

Bid

s

05

1015

0 2 4 6 8 10

05

1015

Seller Advantage: Weak

Values

Bid

s

05

1015

0 2 4 6 8 10

05

1015

Buyer Advantage: Weak

Values

Bid

s

Figure 1: Box and whiskers plot of actual bids-S20 treatment

Figures 1 and 2 describe bids as a function of values using box and whiskers plots

7The numbers in the second column represent value intervals for the weak and strong bidders. Forthe buyer-advantaged regime, the bidding strategies become non-linear for values greater than 6.67 inthe S20 treatment and greater than 4 in the S40 treatment. For the strong bidder, the relevant valuesare 13.34 and 16 for the two treatments, respectively. The value intervals are constructed to account forthese cutoffs while splitting the remaining value intervals equally to achieve a reasonable spread.

8We compare average and median bids by player types to find, once again, evidence of higher biddingunder the seller-advantaged resale than under the buyer-advantaged resale. All results are robust to theexclusion of sessions with low number of participants (n=4,6).

12

010

2030

40

0 8 16 24 32 40

010

2030

40

Seller Advantage: Strong

Values

Bid

s

010

2030

40

0 8 16 24 32 40

010

2030

40

Buyer Advantage: Strong

Values

Bid

s

05

1015

0 2 4 6 8 10

05

1015

Seller Advantage: Weak

Values

Bid

s

05

1015

0 2 4 6 8 10

05

1015

Buyer Advantage: Weak

Values

Bid

s

Figure 2: Box and whiskers plot of actual bids-S40 treatment

for the S20 and S40 treatments respectively. Graphs are separated by bidder type and

resale regime. The boxes represent the interquartile range and the whiskers extend up

to the outermost data point within 1.5 times the interquartile range. The solid lines

represent equilibrium bids, and the dashed lines indicate bids equal to values. Overall,

the box plots are consistent with the descriptive statistics showing relatively higher

bids and greater dispersion for the seller-advantaged resale regime and more so as the

asymmetries intensify. Strong bidders bid on average above their equilibrium bids and

shade their bids more at higher values. Since bidding higher than the weak bidder’s

highest equilibrium bid is a dominated strategy for the strong bidder, the observed

pattern of bids tapering off for the strong bidder is consistent with the previous studies

(Gueth et al. [6]) of one stage asymmetric auctions.

Overbidding compared to equilibrium level is a commonly observed phenomenon

in the experimental literature (Kagel and Roth [13]). It is also seen in these graphs,

13

and it is more pronounced among strong bidders. Weak bidders9 tend to bid closer

to their equilibrium bids except at the lower end of the value distribution under the

seller-advantaged resale regime.

4.2 Bid Deviation from Value under the Prospect of Resale

The equilibrium bidding strategies under a first price auction imply some degree of bid

deviation from value10, calculated as vi − bivi for each bidder i. While the equilibriumbidding strategies under seller-advantaged resale require a constant proportion of bid

deviation for both types of bidders, those under buyer-advantaged resale require a higher

proportion of bid deviation at higher values. In Table 3, we present the average degree

Table 3: Average Degree of Bid Deviation from Value

Player Type Value Block Seller Advantage Buyer AdvantageS20 Treatment

Bid Deviation (vi−bivi ) Actual Predicted Actual Predicted

Weak0 - 3.34 -3.15 0.25 -2.95 0.253.34 - 6.67 -0.05 0.25 0.08 0.256.67 - 10 0.10 0.25 0.15 0.28

Strong0 - 6.67 0.17 0.62 0.30 0.626.67 - 13.34 0.32 0.62 0.37 0.6213.34 - 20 0.42 0.62 0.52 0.64

S40 Treatment

Weak0 - 4 -5.52 -0.25 -0.59 -0.254 - 7 -0.24 -0.25 0.12 -0.157 - 10 -0.13 -0.25 0.11 0.10

Strong0 - 16 0.10 0.69 0.37 0.6916 - 28 0.48 0.69 0.59 0.7128 - 40 0.50 0.69 0.64 0.77

of actual and predicted (in parentheses) bid deviations from value under both resale

regimes for the two treatments. Weak bidders with lower values, on average, bid above

their values under both resale regimes. Strong bidders do not bid above their values.

Under the buyer-advantaged resale, with only one exception, the empirical observations

are both qualitatively and quantitatively closer to the equilibrium predictions than in

the seller-advantaged resale case.

9Georganas and Kagel attribute underbidding by weak types to negative profits for greater disparityamong value distributions.

10It is usually referred to as bid ‘shading’. However, in this case the equilibrium bids could be aboveor below the value. Hence we use the term ‘bid deviation’ here instead. We thank referee for thissuggestion.

14

4.3 Symmetrization of Bid Distributions

An important property of the equilibrium is the symmetrization of bid distributions

under both regimes. The underlying idea is that both weak and strong bidders treat

the auction with resale as equivalent to an auction without resale that has a common

value component determined by the resale stage structure. Hence, we expect the bid

distributions for weak and strong bidders within a given resale structure to be the same.

0 5 10 15 20

0.00

0.04

0.08

0.12

Bids

Den

sity

S20: Seller Advantage

0 5 10 15 20

0.00

0.05

0.10

0.15

Bids

Den

sity

S20: Buyer Advantage

0 10 20 30 40

0.00

0.02

0.04

0.06

0.08

0.10

Bids

Den

sity

S40: Seller Advantage

0 10 20 30 40

0.00

0.04

0.08

0.12

Bids

Den

sity

S40: Buyer Advantage

Strong BidderWeak Bidder

Figure 3: Kernel density estimates for bid distributions. The solid line represents weakbidders and the dashed line represents strong bidders.

The kernel density estimates of bid distributions for weak and strong bidders under

the seller-advantaged and buyer-advantaged regimes in the S20 and S40 treatments are

depicted in Figure 3. The bidding distributions under seller-advantaged resale for the

S20 treatment (top-left panel) exhibit close similarities to those in Georganas and Kagel

[5].11 The bid distributions for weak and strong bidders are much closer under the buyer-

11Georganas and Kagel reject the symmetrization property for sufficiently large asymmetries similarto the level existing here in S20.

15

advantaged regime than under the seller-advantaged regime (see the top-right panel). A

possible reason for this could be the lack of significant speculative motive on the bidder’s

part in the first stage. The two bottom panels show kernel density estimates of the bid

distributions for the two bidder types under each regime for the S40 treatment. The

bid distributions for weak and strong bidders appear quite distinct. A Kolmogorov-

Smirnov (K-S) test provides formal evidence of differences in size, dispersion or central

tendency. The test rejects the null of no difference between weak and strong type bidder

distributions for both regimes and both treatments at a probability value less than one

percent.12

The analysis so far has explored qualitative distributional differences without pro-

viding controls for bidder and auction heterogeneity. Next, we present a quantitative

analysis that controls for unobserved heterogeneity among bidders and differences in

auction and bidder measurable characteristics. We first perform mean level analysis

and then apply quantile regression techniques to investigate how bidding aggressive-

ness varies for different values and types of bidders across the distribution. The basic

econometric model of the relation between values and bids for both bidder types that is

derived directly from the equilibrium strategies is

biat = β1viat + β2(viat ×Ai) + z′iatδ + uiat (1)

where the unit of observation is a bid submitted by bidder i, in auction a, in round t of

a session. Our dependent variable is the bid biat. The value of the bidder i in auction a,

and round t is viat. Ai is an indicator variable that takes value 0 or 1 for a strong and

weak type bidder, respectively. Hence, the coefficient β2 measures the differential effect

of values on bids between a weak and a strong bidder. The vector z contains a set of

variables used to control for observed heterogeneity across bidders and auctions. They

capture a bidder’s attitude toward risk, his/her gender, academic level and previous

participation in real life auctions. It includes indicators of the order of an auction in the

experimental sequence, and the number of available bidders of each type in a session.

We use a random effects model with uiat = �iat + αi. Considering the possibility that

the standard errors may be underestimated (Moulton [19]), we report ‘cluster-robust’

12We tested the normalized (relative) bid distributions to control for differences in the theoreticaldistribution of bids. They yield similar results.

16

standard errors where the clustering is done by players.13 The coefficients of our interest

are β1 and β2. As mentioned in section 2, weak bidders bid twice as much as strong

bidders in the S20 treatment and four times as much in the S40 treatment. Hence,

we expect β1 = β2 in the S20 treatment under each regime and β2 = 3β1 in the S40

treatment.

Table 4: Mean level and quantile regression results for actual bids

Quantiles Mean LevelVariables 0.25 0.5 0.75

Treatment S20 Seller-advantaged ResaleValue(β1) 0.489* 0.534* 0.589* 0.499*

(0.014) (0.019) (0.025) (0.031)Value × Weak Bidder Indicator 0.331* 0.323* 0.272* 0.228*(β2) (0.023) (0.025) (0.032) (0.038)

p-value from testing H0 : β2 = β1 0.000 0.000 0.000 0.000

Treatment S20 Buyer-advantaged ResaleValue(β1) 0.394* 0.404* 0.443* 0.402*

(0.019) (0.021) (0.032) (0.031)Value × Weak Bidder Indicator 0.401* 0.424* 0.389* 0.306*(β2) (0.025) (0.028) (0.037) (0.048)

p-value from testing H0 : β2 = β1 0.858 0.658 0.417 0.167

Treatment S40 Seller-advantaged ResaleValue(β1) 0.303* 0.346* 0.435* 0.427*

(0.029) (0.032) (0.056) (0.056)Value × Weak Bidder Indicator 0.569* 0.546* 0.411* 0.395*(β2) (0.041) (0.047) (0.074) (0.089)

p-value from testing H0 : β2 = 3β1 0.005 0.000 0.000 0.000

Treatment S40 Buyer-advantaged ResaleValue(β1) 0.200* 0.242* 0.267* 0.302*

(0.022) (0.023) (0.022) (0.044)Value × Weak Bidder Indicator 0.578* 0.626* 0.596* 0.472*(β2) (0.040) (0.034) (0.037) (0.070)

p-value from testing H0 : β2 = 3β1 0.810 0.315 0.030 0.017

Standard errors are in parentheses. * denotes statistical significance at the 1% level. N = 1348 for S20

SA Resale, N = 1358 for BA Resale. N = 1080 for S40 SA Resale and S40 BA Resale.

A simple quantile regression model allows us to investigate more systematically how

13We estimated the model using both fixed effects and random effects. A Hausman specification testindicated that the preferred model was the random effects model.

17

the effect of key controls varies across the conditional distribution of bids reducing the

impact of outlier values. Since there is a differential effect by bidder type upon bids

across the value distribution, the model can shed light on symmetrization property.

Following Koenker and Bassett [14] and Koenker [15] we propose the following simple

quantile regression model:

Qbiat(τ |xiat) = xiatγ(τ) (2)

where Q(.|.) is the τ -th conditional quantile function, γ(τ) = (β1(τ), β2(τ), δ(τ)′)′ is thevector of parameters and xi = [viat, viat ×Ai, z′iat] is the vector of covariates.

The quantile model is estimated via optimization by finding

γ̂(τ) = argmin∑i

∑a

∑t

ρτ (biat − x′iatγ(τ)) (3)

where ρτ (u) = u(τ − I(u < 0)) is the quantile regression “check function.” We restrictattention to three quantiles (τ = 0.25, 0.50, 0.75).

In Table 4, we report mean level and quantile regression results for bids in the seller-

advantaged and buyer-advantaged regimes under the S20 and S40 treatments. We use

F-tests of the difference in bidding intensity between strong and weak bidders under the

two regimes to test for symmetrization.14 Our results suggest that there is no support

for this theory for the seller-advantaged resale regime, and that is consistent with other

findings featuring similar level of asymmetries (Georganas and Kagel’s [5]). We find,

however, evidence of symmetrization under the buyer-advantaged resale regime in the

S20 treatment. In the S40 treatment, the conditional quantile regression results based

on 0.25, 0.5 quantile estimates suggest that bidding distributions are identical for low

value bidders but a look at the mean and upper quantile regression estimates makes

apparent that this pattern is breaking down for bidders with high values.

4.4 Resale Price Comparisons

According to Proposition 1, we expect higher resale prices under the seller-advantaged

resale regime compared to the buyer-advantaged resale regime. The disparity in resale

prices can be perceived as an indication of speculative behavior on the part of the weak

bidder under the seller-advantaged resale regime that is significantly reduced in the

14As mentioned earlier, the hypotheses tested are that β2 = β1 and β2 = 3β1 for the S20 and the S40treatment respectively.

18

0 5 10 15 20

0.00

0.10

0.20

S20: Seller Advantage

Bids/Prices

Den

sity

Bid:WeakBid:StrongResale Price

0 10 20 30 40

0.00

0.05

0.10

0.15

S40: Seller Advantage

Bids/Prices

Den

sity

Bid:WeakBid:StrongResale Price

0 5 10 15 20

0.00

0.10

0.20

S20: Buyer Advantage

Bids/Prices

Den

sity

Bid:WeakBid:StrongResale Price

0 10 20 30 400.

000.

050.

100.

15

S40: Buyer Advantage

Bids/Prices

Den

sity

Bid:WeakBid:StrongResale Price

0 5 10 15 20

0.0

0.4

0.8

S20: Resale Prices

Resale Prices

F(P

)

Seller AdvantageBuyer Advantage

0 5 10 15 20 25 30

0.0

0.4

0.8

S40: Resale Prices

Resale Prices

F(p

)

Seller AdvantageBuyer Advantage

Figure 4: Comparing auction and resale prices across resale regimes

buyer-advantaged resale regime. The top four panels of Figure 4 show the kernel density

estimates of auction and resale prices by treatment and resale regimes.

The average realized (predicted) prices in the seller-advantaged resale regime are 8.17

(7.5) in the S20 treatment and 12.37(12.5) in the S40 treatment. The corresponding

prices in the buyer-advantaged resale regime are 6.75 (6.67) and 8.0815 (8.00) respec-

tively. Final prices are expected to increase on average by 12.44% - 56.25% depending

on the treatment. The final price differences across regimes are not matched by final effi-

ciency reductions when one moves from the buyer to the seller-advantaged resale regime

as we will show in the next section. The probability distribution functions in the bottom

15Seemingly higher auction prices (winning bids) in S40 buyer advantaged resale are driven by a fewhigh bids in auctions that did not result in resale.

19

2 panels of figure 4 present a better- more direct- picture of differences among realized

prices across regimes. It becomes obvious that there is a greater likelihood of high prices

in the seller-advantaged resale regime. The experimental data shows higher resale prices

on average under seller-advantaged resale as expected and provides support for Propo-

sition 1. For the S20 treatment, on average, the resale price is 33% higher under the

seller-advantaged resale than under buyer-advantaged resale conditional upon trade in

the resale stage (p-value = 0.0000). For the S40 treatment, the average resale price

conditional on trade at the resale stage is about 28% higher under the seller-advantaged

resale than under the buyer-advantaged resale (p-value = 0.0012). We further employ

Mann-Whitney tests to compare the equality of resale price distributions under the

seller-advantaged and the buyer-advantaged resale conditional upon trading at the re-

sale stage. The null of equality of resale prices is rejected for both the S20 (p-value =

0.0032) and the S40 (p-value = 0.0104) treatments.

4.5 Efficiency Comparisons

We consider two definitions of efficiency. In the first definition (E-1), we use the ratio of

number of outcomes wherein a high value bidder wins to the total number of outcomes.

In Table 5, we describe the interim (auction stage) and final (resale stage) efficiency

comparisons for both treatments using data from all periods.16 Interim efficiency is

predicted to be the same while expected final efficiency is reduced by 4.54%-12.16% in

the seller-advantaged regime depending on the treatment. Interim efficiency is higher

than predicted but almost equal across regimes for the S20 treatment. The final efficiency

levels are also similar with the seller-advantaged resale registering higher actual efficiency

than predicted. For the S40 treatment, interim efficiency for both regimes is much higher

than predicted. Final efficiency for the buyer-advantaged resale is relatively higher

providing support for Proposition 2 only in this case.

We also report efficiency calculations based on another widely used measure. This

definition (E-2) employs the average value of the ratio vimax{vi,v−i} , where the numerator,

vi, is the owner’s value at a given stage and the denominator is the maximum of the

values of everyone else who is part of the market at that stage. Unlike E-1, which

relies on the count of efficient versus inefficient outcomes, E-2 focuses on the average

magnitude of realized surplus. In Table 6, we report the predicted and actual efficiencies

16The calculations for both tables using periods 11 - 20 are consistent with these numbers.

20

Table 5: Allocative efficiency (E-1) in percent

Interim Final

Predicted Actual Predicted Actual

S20 Seller Advantage 75.00 80.71 87.50 90.80S20 Buyer Advantage 75.00 80.11 91.67 90.42

S40 Seller Advantage 62.50 77.03 81.25 87.96S40 Buyer Advantage 62.50 79.25 92.50 92.78

Table 6: Efficiency measured by realized surplus (E-2) in percent

Interim Final

Predicted Actual Predicted Actual

S20 Seller Advantage 91.67 91.37 97.56 96.40S20 Buyer Advantage 92.07 91.73 99.00 96.91

S40 Seller Advantage 79.70 85.66 93.25 93.64S40 Buyer Advantage 81.06 89.34 98.38 97.34

based on this approach. Actual interim efficiencies for the S20 treatment are about

the same across regimes and similar to the predictions. Actual final efficiencies are

also similar in magnitude for the two regimes but lower than predicted. For the S40

treatment, the observed interim efficiencies are higher than predicted and even more so

for the buyer-advantaged resale. The observed final efficiencies are much closer to the

predictions, implying a higher lost surplus under the seller-advantaged resale compared

to the buyer-advantaged resale.

Higher than predicted interim efficiency is the result of strong (weak) type bidders

bidding higher (lower) than the equilibrium level precluding the need for resale. Getting

a closer look at the price-efficiency trade-off, in selecting a bidding strategy one takes into

account the likelihood of missing a beneficial trade opportunity which has a high cost

(in terms of lost value) across regimes. On the other hand, distributional asymmetries

across bidder types generate an upper bound for prices only in the buyer- advantaged

resale case increasing price differentials across regimes. The result is a highly variable

price but not much of a difference in final efficiency.

21

5 Conclusions

We derive equilibrium bidding distributions in an auction with the buyer-advantaged

resale and compare them to those derived in Hafalir and Krishna [7] for auctions with

seller-advantaged resale. The shift of bargaining power from seller to buyer tends to

reduce speculative tendencies on the bidder’s part, leading to differential revenue and

efficiency outcomes. Our experimental results show that bids are indeed higher under

the seller-advantaged resale regime than the buyer-advantaged resale regime across both

treatments and the bid differential ranges between 12.31% and 33.64%. The average

winning bids under seller (buyer) advantage for the S20 and the S40 treatments are 7.61

(6.73) and 12.22 (9.15), respectively. The average auction and resale prices are higher

under seller-advantaged resale while this increase in prices is not matched by efficiency

reductions.

Our model predicts that when the buyer has complete advantage in the resale market,

the average auction and resale prices are the lowest. Despite the fact that the model

and experimental evidence is on limiting cases of bargaining power distribution, the

comparative static predictions are reflected in the course of RGGI prices over the last

five years.17 In Figure 5, we see relatively higher ratio of the number of bids to the

number of allowances at the beginning of the RGGI program reflecting a seller’s market.

The opposite trend is observed from December 2009 through December 2012 with a

reversal since then. Resale market prices track auction prices very closely even more so

when the seller’s power is diminishing. Our theory and experimental evidence shed some

light into bids, prices and expectations for market efficiency. While prices are expected

to fluctuate significantly as market power shifts hands, inefficiencies are not expected to

either be significant or vary widely.

In our experiments, the actual number of efficient outcomes, both interim and fi-

nal, are higher than predicted by the theory generating small differences in allocative

efficiency across regimes (between 0.38-4.82%). Across all cases considered, the mini-

mum amount of surplus realized is still no less than 93.64%. Our quantitative analysis,

providing controls for bidder and auction level characteristics, offers some support to

symmetrization only in the buyer-advantaged case. In highly asymmetric cases though,

high value weak and strong bidders differentiate their bidding strategies.

17The proof of the continuity in the price/bidding- efficiency tradeoff as we vary the distribution ofbargaining power between these extreme cases can be provided by the authors upon request.

22

Figure 5: Selected trends from RGGI Allowance Auctions

2009 2010 2011 2012 2013

01

23

4

Selected Trends from RGGI Allowance Auctions: 2008−2013

Year

Ratio of Bids to SupplyAuction Clearing Price($)CCFE futures price($)

Source: RGGI Market Monitor, Various Reports.

6 Appendix

6.1 Equilibrium Bid Distributions under the buyer-advantaged Resale

Proof. Our setup is the same as in Hafalir and Krishna [7]. There are two risk neutral

bidders, bidding in an auction with the possibility of resale having no liquidity con-

straints. Bidder i’s private value is drawn from a regular distribution, Fi, with virtual

valuation equal to xi − 1−Fi(x)fi(x) , that is increasing in x, where Fi, i = s, w is the valuedistribution for bidder i. Given this setup, resale happens invariably from the weak to

the strong bidder. The idea that converts this two stage game into a single stage equiv-

alent auction is the symmetrization property. Assuming that Fs(x) < Fw(x) for all x,

the first price asymmetric auction with resale (FPAR) is characterized by the following

system of differential equations

d

dblnFk[φk(b)] =

1

p(b)− bφk(0) = 0 φk(b̄) = ak ∀k = s, w. (4)

It is the same as a first price symmetric auction without resale (FPWR) characterized

byd

dblnF [φ(b)] =

1

φ(b)− b(5)

23

where F (.) is the common distribution derived from Fs and Fw defined over [0, p̄]. With

p̄ as the upper bound of the price in the resale stage, we derive b̄, the highest bid and

then we can solve for bidding functions from the system of differential equations in (7).

The problem under the buyer-advantaged regime can be tackled in a similar way.

For the purpose of exposition, we refer to weak bidder as “he” and strong bidder as

“she” in the following discussion. Note that the weak bidder does not have any control

over the resale price. He can only accept or reject the offer made by his opponent. The

strong bidder knows her own bid, her private value, and the upper bound of the weak

bidder’s value distribution. The weak bidder’s value distribution is [0, aw] and aw < as,

by assumption. Hence, it will be suboptimal to offer anything above aw since all offers

above this threshold are strictly dominated. Therefore, the resale price will be drawn

from an interval [0, aw], which is the same as the weak bidder’s value distribution. Using

the idea of equivalence, and given Fs and Fw with Fs(x) < Fw(x) for all x, the first

price asymmetric auction with resale (FPAR) is characterized by the following system

of differential equations

d

dblnFk[φk(b)] =

1

r(b)− bφk(0) = 0 φk(b̄) = ak ∀k = s, w (6)

is equivalent to a first price symmetric auction without resale (FPWR) characterized by

d

dblnFw(.) =

1

φ(b)− b(7)

with Fw(.) the common distribution over [0, aw].

For r ≤ aw, the solution satisfies the system of differential equations

d

dblnFk[φk(b)] =

1

r(b)− b∀k = s, w (8)

subject to the following boundary conditions:

φk(0) = 0, φs

(aw2

)=

2awasaw + as

, φw

(aw2

)=

2a2waw + as

.

For r = aw, the solution satisfies the system of differential equations

d

dblnFk[φk(b)] =

1

aw − b∀k = s, w (9)

24

subject to the following boundary conditions:

φs

(aw2

)=

2awasaw + as

φw

(aw2

)=

2a2waw + as

φs

(awasaw + as

)= as φw

(awasaw + as

)= aw.

6.2 Proposition 1

Proof. Using the mean value theorem, the average value of bid function for the seller

advantaged resale is: ∫ ai0

aw+as4ai

xdx

ai − 0=aw + as

8∀i = w, s.

For the buyer advantaged resale, average value of the bid function is:

∫ 2awasaw+as0

(aw+as4as

)xdx+

∫ as2awasaw+as

(aw − a

2was

x(aw+as)

)dx

as − 0

=aw [2as − aw + awLog(4) + 2awLog(aw)− 2awLog(aw + as)]

2(aw + as).

It would suffice to show that the difference between these two expressions is increasing

for all as > aw. The derivative of this difference with respect to as is:

1

8+a2w

(Log[aw] + Log

[aw

as+aw

]− Log

[a2w

as+aw

])(as + aw)2

> 0 ∀as > aw.

Since the bid functions for weak and strong bidders are proportional, a similar exercise

would yield identical answers for the weak bidder’s case under both resale structures.

The proof of higher average resale prices follows a similar reasoning. For seller advan-

taged resale, the average resale price is:

1

aw

∫ aw0

aw + as2aw

xdx =as + aw

4. (10)

25

For buyer advantaged resale, it is:

1

as

(∫ 2awasas+aw

0

aw + as2as

xdx+

∫ as2awasas+aw

awdx

)=

asawas + aw

. (11)

Subtracting (11) from (10) gives

(as − aw)(as + 3aw)4(as + aw)2

> 0 ∀as > aw.

6.3 Proposition 2

Proof. Using the equilibrium bidding strategies, the likelihood of a strong type bidder

winning the auction stage under seller-advantaged resale is:

1

awas

∫ aw0

∫ as2vw

dvsdvw. (12)

Under a buyer-advantaged resale, the likelihood of a strong type bidder winning the

auction stage is:

1

awas

∫ 2a2was+aw

0

∫ 2awasas+aw

2vw

dvsdvw +1

awas

∫ 2a2was+aw

0

∫ as2awasas+aw

dvsdvw

+1

awas

∫ aw2a2w

as+aw

∫ 2awasas+aw

0dvsdvw +

1

awas

∫ aw2a2w

as+aw

∫ as2vw

dvsdvw. (13)

The likelihood of a strong type having a value higher than the weak type is:

1

awas

∫ aw0

∫ awvw

dvsdvw. (14)

Thus, interim inefficiency18 is calculated as the difference between (14) and (12) in

the seller-advantaged resale regime and (14) and (13) in the buyer-advantaged resale

regime. Showing that interim inefficiency under any of the regimes is exactly the same

requires us to show that expressions (12) and (13) are identical. Subtracting (13) from

(12) yields this result.

18Interim efficiency is obtained by subtracting interim inefficiency from unity.

26

The likelihood of strong bidder not accepting the offer and having a value higher than

weak bidder constitutes final inefficiency under the seller advantaged resale. It is given

by

Pr.(2bw > vs > vw) =1

awas

∫ aw0

∫ as+aw2aw

vw

vw

dvsdvw =1

4− aw

4as.

Holding aw constant, as as →∞, the final inefficiency converges to 14 in the limit.The final inefficiency under the buyer-advantaged resale is given by the likelihood of a

weak bidder not accepting the offer and having a value lower than the strong bidder. It

is calculated as

Pr.(vs > vw > 2bs) =

1

awas

∫ aw0

∫ vsas+aw

2asvs

dvsdvw =1

awas

∫ 2asawas+aw

aw

∫ awas+aw

2asvs

dvwdvs =aw(as − aw)2as(as + aw)

.

Holding aw constant, as as →∞, the final inefficiency goes to 0 in the limit.Hence, the seller advantaged resale structure leads to the lowest number of (predicted)

trades, whereas the buyer advantaged resale structure leads to the highest number of

(predicted) trades in the resale stage. This leads to the respective levels of predicted

final efficiencies and completes the proof.

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INSTRUCTIONS:

This is an experiment regarding auctions. If you follow the instructions carefully, youmight earn money that will be credited to your sooner sense account. The participation ispurely voluntary. If you decide to participate, you will get 65 Ruchmas (our experimentalcurrency) that will serve as initial capital (or endowment) for you in addition to whatyou earn during the experiment. Ruchmas will be converted to Dollars at a rate of13 Ruchmas = $1. The expected duration of experiment is about 90 minutes. I amgoing to read out the instructions before we begin.

• You will act as a potential buyer bidding for 20 fictitious commodities sold insuccessive rounds.

• At the beginning of the experiment, a random flip of a coin will determine if youare going to be “Bidder type-U” or “Bidder type-P”. Please note that your typewill remain the SAME throughout the experiment.

• In each successive round, you will be matched with a different opponent who isNOT your type. [for example, if you are Bidder type-U, your opponent will alwaysbe a Bidder type-P and vice versa]

• Your opponent will change for each successive round but they will all be of thesame type (and that is different than your type).

• In each successive round, you will be matched with a different opponent who isNOT your type. [for example, if you are Bidder type-U, your opponent will alwaysbe a Bidder type-P and vice versa]

• Your opponent will change for each successive round but they will all be of thesame type (and that is different than your type).

• In each round, the value of the commodity for a bidder type-U will be a randomnumber up to two decimal places between 0.00 and 10.00 Ruchmas (that is, anyvalue between 0.00 and 10.00 is equally likely). FIGURE 1 describes the likelihoodof all possible values for bidder type-U. So your value is the result of a spin of thearrow attached to this wheel for every round.

• Similarly, in each round, the value of the commodity for a bidder type-P will be arandom number up to two decimal places between 0.00 and 20.00 Ruchmas (thatis, any value between 0.00 and 20.00 is equally likely). FIGURE 2 describes thelikelihood of all possible values for bidder type-P. So your value is the result of aspin of the arrow attached to this wheel for every round.

• Each round will have two stages: The Auction Stage and The Resale Stage. Hereis how a typical round will proceed:

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Figure 1: Value Distribution for BIDDER TYPE U

Figure 2: Value Distribution for BIDDER TYPE P

• To summarize, your type remains the same in today’s session (it is eitherP or U) but your value may change in every round. Your value for eachround is determined by a spin of the arrow. Please note that every spinis independent.

• You will be reminded of your type at the beginning of every new round.

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Stage I-The Auction Stage:In this stage, every player will submit a bid for a fictitious commodity being sold at

an auction.

• You will receive the information about your value only.• After finding out your value for the commodity, you will begin by choosing a

number or a “bid”. Please think carefully before you make your choice. You mayuse a calculator by clicking on the icon that will appear to the right hand side ofyour screen. You will have 45 seconds to make a decision. Your Opponent willalso choose a bid at the same time. Neither player can see his opponent’s value orbid.

• The person with the high bid will win the commodity being sold and pay his ownbid as the price. In the case of a tie, a random coin flip will decide the winner.

• You will be informed whether you won the auction or not.• The following schematic describes the auction stage and the interim payoff calcu-

lations.

• Note that this is just the interim payoff. The final payoff of a round will be deter-mined at the end of stage II- the Resale Stage. It will begin immediately after theauction stage.

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Stage II-The Resale Stage (Owner Makes An Offer):In this stage, the bidder who won the first stage will have the opportunity to

resell the commodity to his opponent. It works in the following way:

• The winning bidder can choose to make a ‘take-it-or-leave-it’ offer to the opponent.• If the winning bidder does not want to make an offer, he may quote a price of 9999

Ruchmas.

• If the offer is made and accepted, trade takes place and the owner will receive thedifference between the offer and his first stage bid. The opponent will receive thedifference between his value and the offer.

• If the offer is rejected (or is 9999) there will be NO trade in the second stage. So,the first stage winner will keep the commodity and receive the difference betweenhis value and the first stage bid. The opponent will receive nothing for that round.

• The following schematic describes the course of the second stage where the ownermakes an offer:

• This will conclude a typical round and a new round will begin with Stage I asdescribed earlier.

• The total earnings for a player will be equal to the SUM of all final payoffs fromeach round. The dollar amount to be credited on your sooner sense account willbe calculated on the basis of the conversion rate mentioned earlier.

• Are there any questions at this stage? Please feel free to ask before we begin.

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• The following graphical example will show how a typical round will proceed:

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Stage II-The Resale Stage (Owner Receives An Offer):In this stage, the bidder who did not win the first stage will have the opportunity

to buy the commodity from his opponent. It works in the following way:

• The bidder not winning the first stage can choose to make a ‘take-it-or-leave-it’offer to the opponent.

• If he does not want to make an offer, he may quote a price of 0 (Zero) Ruchmas.• If the offer is made and accepted, trade takes place and the owner will receive the

difference between the offer and his first stage bid. The opponent will receive thedifference between his value and the offer.

• If the offer is rejected (or is 0) there will be NO trade in the second stage. So, thefirst stage winner will keep the commodity and receive the difference between hisvalue and the first stage bid. The opponent will receive nothing for that round.

• The following schematic describes the course of the second stage where the ownermakes an offer:

• This will conclude a typical round and a new round will begin with Stage I asdescribed earlier.

• The total earnings for a player will be equal to the SUM of all final payoffs fromeach round. The dollar amount to be credited on your sooner sense account willbe calculated on the basis of the conversion rate mentioned earlier.

• Are there any questions at this stage? Please feel free to ask before we begin.

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• The following graphical example will show how a typical round will proceed:

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IntroductionRelated Literature

Theoretical FrameworkExperimental DesignResults And DiscussionDescriptive StatisticsBid Deviation from Value under the Prospect of ResaleSymmetrization of Bid DistributionsResale Price ComparisonsEfficiency Comparisons

ConclusionsAppendixEquilibrium Bid Distributions under the buyer-advantaged ResaleProposition 1Proposition 2

References