price improving

Price Improvement in Dealership MarketsAuthor(s): Matthew RhodesKropfSource: The Journal of Business, Vol. 78, No. 4 (July 2005), pp. 1137-1172Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/10.1086/430857 .Accessed: 08/05/2015 07:56

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#05507 UCP: JB article # 780402

Matthew Rhodes-KropfGraduate School of Business, Columbia University

Price Improvementin Dealership Markets*

I. Introduction

To understand price formation we must understandprice improvements and why improvements aregiven. Price improvements may be given to cus-tomers with less information. This is the standardtheory in market microstructure initially formal-ized by Seppi (1990). However, it may be thatsome customers have different amounts of mar-ket power due to their size, knowledge, technol-ogy, discount rate, and the like, regardless of theirinformation. Those customers with more marketpower negotiate better prices. The introduction ofthis second theory is important both to under-stand price improvement and to regulate marketsbut also because it recognizes that financial mar-kets may not be perfectly competitive and there-fore the market power of customers relative todealers may play a significant role in the forma-tion of prices.The simultaneous examination of both models

demonstrates the effects of price improvementthat are general and those that depend on the spe-cific reason improvements are given (adverse se-lection or market power). This comparison resultsin predictions that can be empirically tested to

(Journal of Business, 2005, vol. 78, no. 4)B 2005 by The University of Chicago. All rights reserved.0021-9398/2005/7804-0002$10.00

1137

* This paper is based on my dissertation at Duke University.I am grateful for the exceptional guidance of S. Viswanathanand Larry Glosten. Helpful comments were also provided byJames Anton, Robert Jennings, Charles Jones, Eugene Kandel,Ken Kavajecz, Costis Maglaras, Georg Noldeke, Tavy Ronen,Nikolaos Vettas and an insightful referee, as well as participantsin seminars at the SFS conference on Price Fromation, NBER,Columbia, Indiana, Michigan, the SEC and UNC. All errors aremy own.

Price improvementrefers to the practicewhereby dealersoffer executions thatimprove on quotedprices. Why are theseimprovements given?Standard thinking isthat competition causesdealers to give betterprices to customerswith less information.This paper contraststhis with a novel theoryin which customersnegotiate improvementsand differential pricingarises from differencesin customers marketpower. Each theoryaffects the formationof bid /ask spreadsin empiricallydistinguishable ways.Understanding priceimprovement and itsimpact on marketparticipants is criticalthe regulation ofmarkets, particularlysince equal executionis such an importantstated goal of the SEC.


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determine the dominant explanation for price improvements. Sinceequal execution is an important goal of the regulatory process an un-derstanding of why execution may be unequal is critical. Furthermore,price improvements and market power may be important unexaminedcomponents of the bid/ask spread.Price improvement is a pervasive feature of many financial markets,

especially dealer markets such as the NASDAQ and London equitymarkets and the foreign exchange market. Furthermore, almost all newfinancial innovations are traded through dealer markets. In London,evidence provided by Reiss and Werner (1996) and Hansch, Naik, andViswanathan (1999) shows that mid-size and large trades receive aprice improvement over small trades. This practice is controversial, as itimplies that customers that are able to negotiate may be able to obtainbetter executions than other customers. On NASDAQ, the ability tonegotiate posted quotes has been suggested by Kleidon and Willing(1995) and Grossman et al. (1997) as an important reason spreads on theNASDAQ market are so wide, as documented in Christie and Schultz(1994). Even auction-type markets like the New York Stock Exchange(NYSE) feature price improvement on the best quotes through hiddenlimit orders or stopped orders, as documented in Petersen and Fialkowski(1994) and Ready (1999). However, none of these papers model howquotes are determined in the presence of price improvement.In the canonical models of market microstructure laid out in Kyle

(1985, 1989), Glosten and Milgrom (1985), and Ho and Stoll (1983),price improvement is not considered and market makers expect zeroprofit from each trade. However, in this paper, as in Dennert (1993),dealers expect profits on individual trades (though, with fixed costs,the expected market-making profit may still be zero). Thus, dealers havethe market power to set the spread wider than the zero-expected-profit-per-trade prices.1 This gives them room to give price improvements.Less-than-perfect competition among dealers is modeled by allowing

heterogeneous dealers to choose bids in a first price auction.2 Whilebidding for order flow due to dealer heterogeneity is allowed in Ho andStoll (1983)3 and Biais (1993), the best quotes in these models are the

1. On SEAQ, the average number of dealers per stock ranges from 12.6 for the FTSE-100to 6.2 and 4.7 for the medium and small equities (Reiss and Werner 1996). Furthermore, forthe FTSE-100, seven dealers execute 90% of public orders (Hansch, Naik, and Viswanathan1998). On NASDAQ, the average number of dealers is 10, although some stock have only1 and others have over 60. Therefore, lessthan-perfect competition seems a reasonable char-acterization of these markets.2. The use of the auction model is not meant to suggest that dealer markets are exactly like

auctions, in the same way that Kyle (1989) is not meant to suggest that orders are batched.Rather, an auction model is used because dealer markets have similarities to an auction. Whatan auction model sacrifices in reality it makes up for in tractability and with insightful results.3. Ho and Stoll (1983) is effectively a form of English auction, as the spread is defined by

the reservation value of the second-highest dealer. However, under particular conditions thereservation value of every dealer is the same in equilibrium.

1138 Journal of Business


#05507 UCP: JB article # 780402

prices at which trades are executed. However, dealership markets arecharacterized by the posting of wide quotes followed by price improve-ment to some customers. In this paper, unlike a standard first price auc-tion, where no negotiation of bids is allowed, a fraction of customersreceive a price better than the first-stage dealer quotes.The first model considered here develops information-based price

improvement and originates from the theories proposed by Seppi (1990),Barclay and Warner (1993), and Hansch et al. (1999). Seppi (1990) notedthat, with negotiated improvements, the transaction is not anonymous;thus, implicit contracts can bind repeat customers.4 A penalty technol-ogy could force repeat customers to acknowledge when they are informedby trading at the quotes and ask for an improvement only when they areuniformed.5 Competition then forces dealers to give better prices to less-informed customers. Barclay andWarner (1993) and Hansch et al. (1999)suggest that dealers can examine customers to assess their information.So informed customers remain anonymous and trade at the quotes, whilethe uninformed submit to examination and receive an improvement.The result of either theory is the same: less-informed customers receiveprice improvements.The second model considered is novel. In this theory, price improve-

ments are negotiated and determined by the relative market power ofcustomers and dealers. This model relaxes the assumption implicit inany information model, that either the dealers expect zero profit andtherefore could not negotiate or that dealers have all the market powerand thus post take-it-or-leave-it prices. Instead, we assume that somecustomers can make counteroffers to the posted quotes. Since compe-tition between dealers is less than perfect, dealers bid below their truevalue, leaving the surplus up for negotiation. Those customers who cannegotiate may be larger, own a negotiation technology, have lower dis-count rates, posses greater skill, and so forth, but they do not necessarilyhave less or more information than a customer who cannot negotiate.Note that, with information-based improvements, the uninformed

customers receive improvements because competition forces the deal-ers to raise their prices to obtain these more profitable customers. How-ever, in the bargaining model, the market power of the customer requiresthe dealer to give up some surplus even though all customers are equallyprofitable.Either theory affects price formation. Dealers quote prices with the

knowledge that either competition or negotiation may result in an

4. Recent work by Bernhardt et al. (2002) and Desgranges and Foucault (2002) models thisrepeated interaction.5. See Seppi (1990), proposition 2. Seppi also demonstrates a partial-pooling equilibrium,

where some informed customers ask for price improvements. However, even in this equi-librium customers can credibly signal (although imperfectly) that they are uninformed. Forsimplicity, this paper focuses on the separating equilibrium.

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improvement. Focusing first on the similarities between the theoriesclarifies the relevant differences: in both models, an increase in thefraction of informed customers widens the bid/ask spread as in a stan-dard model. An increase in the probability that a customer negotiates orthe market power of a negotiator (in the second model) also widens thebid/ask spread. However, with either form of price improvement, thedealers profits are unaffected by the probability that a customer willnegotiate. The notion that dealers are not affected by price improve-ments seems counterintuitive. Intuition might suggest that, when thedealers are forced to give up some surplus to customers with marketpower, their profits should go down. Or, when the dealers are able todiscriminate based on the customers information, their profits shouldgo up. This is not the case. A more accurate intuition is that, if pricesmay be improved, the dealers post wider quotes but competition amongdealers causes their overall expected profit to remain unchanged.The stability of dealer profits follows from the celebrated revenue

equivalence theorem of Myerson (1981), Harris and Raviv (1981), andRiley and Samuelson (1981). Since the true value of a trade does notchange with the probability that a customer can negotiate and the com-petition is not changing, dealers simply adjust their quotes, in expec-tation, to earn the same amount. This is important because it tells us thatdealers are affected only by changes that alter the size of the availablepie, such as the level of adverse selection, taxes, the quantities negoti-ated, competition, or deadweight costs like negotiation effort. However,the dealers are not affected by the type or level of improvements.The bid/ask spread, however, is wider as a result of price improve-

ments. Therefore, the width of the spread is determined in part by thenegotiators market power. Most research on the components of thespread has examined order-processing costs, inventory-holding costs,and adverse selection costs6 (see Huang and Stoll 1996 for a summaryof the literature). This paper suggests that a fraction of the market spreadis due to price improvements.Since the dealer is not affected by improvements, the first-order

effect of price improvement is simply a transfer between customers.This tells us that the public policy issue is whether one group of trad-ers should gain relative to another group of traders. Price improvementbased on information allows negotiating uninformed customers and in-formed customers to both receive prices commiserate with their infor-mation. Also, if improvements are banned, then informed customersextract even more from the uninformed customers, who cannot negoti-ate. If improvements are due to customers with market power, then theyallow institutional players to extract surplus from the customers who

6. Such as Glosten and Harris (1988) and Foster and Viswanathan (1993).



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cannot negotiate improvements. Thus, this work demonstrates how thecosts and benefits of price improvement depend on the type of priceimprovement.The initial results provide a broad intuition that the type or existence

of price improvement does not affect the dealer. However, the differ-ent models imply different correlations between the quoted and nego-tiated spreads. This paper shows how it may be possible to empiricallydetermine which form of price improvement is dominant in a particularmarket.If the fraction of informed customers in the market increases and

the information model is correct, then the quoted spread should increasebut the improved spread should not. In contrast, if the market power-based model is correct, then both the quoted and negotiated spreadsshould increase. If a proxy could be found for an increase in the prob-ability of negotiation, then a similar test could be run on a change in thisprobability.If we examine how competition affects the price improvements, we

can then find both another test of the models and an interesting expla-nation for a seeming anomaly. In a market with many dealers, the stan-dard prediction is that greater competition forces dealers to increasethe price improvements, see for example Harris (1994). However, Reissand Werner (1996) find the opposite result. They find that the price im-provement on securities for which many dealers make a market is lessthan the price improvement on securities with little competition.Smaller price improvement is the natural outcome of greater dealer

competition if improvements are based on the market power of custom-ers. In the market-power model, greater competition decreases the mag-nitude of the price improvements, because each dealer earns less, so lessis available for negotiators to acquire. However, in the information-basedmodel, greater competition forces dealers to give larger improvements,as expected by Harris (1994). Thus, in the market-power model, im-provements decrease with increased competition, but in the informationmodel, improvements increase with competition. Consequently, Reissand Werners 1996 result lends support to the theory that customer mar-ket power plays a significant role in price formation and suggests thatinformation may not be as important in price improvements.This paper examines two different explanations why dealers give price

improvements. Thus, it provides a better understanding of how prices areformed. Although the focus is on microstructure, the results apply moregenerally to any situation where an item is exchanged through a dealer.Why are improvements given? Is it because some customers are unin-formed or because some customers have market power? We concludethat themarket power of customers is an important and unexplored aspectof market microstructure.



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Section II of this paper presents both models of price improvement.Section III analyzes the general affects of price improvement. Section IVfocuses on the differences between the models and the tests to determinewhich theory is correct, and Section V examines the effect of competi-tion. Section VI concludes.

II. The Model

The securities market is modeled as a three-stage game with private in-formation. In the first stageN risk-neutral dealers post quotes to purchase(bid) and sell (ask) a security.7 In the second stage, a customer arrives. Afraction a of the customers have the potential to receive a price improve-ment through one of two interactions, discussed in detail later. Thosecustomers that receive an improvement trade at the improved price andthose customers that do not receive an improvement trade at the postedquotes. In the third stage, the value of the security is revealed.The dealers have common beliefs about the value of the security.

Dealers also have an independent private characteristic, such as in-ventory positions or variable transaction costs.8 The variable costs en-sure that each dealers willingness to pay for the security, vbi , is belowhis willingness to sell the security, vai , where the subscript representsthe different dealers and the superscript indicates the bid side (b) or theask side (a) of the market. On either side of the market, the individ-ual dealers dollar values accounting for his private characteristics aredistributed independently and identically and drawn from Fbv withFbvb 0;Fbvb 1, orFavwithF ava 0;Fava 1; althoughthe dealers values are independent, clearly an individual dealers will-ingness to buy and sell are not independent. Here, Fav and Fbvare strictly increasing and differentiable over their respective intervalsvb; vb or va; va, with vb < va. The assumption that vb < va is equiv-alent to the assumption that all interdealer trades have already occurredor that trading costs exceed the benefits of interdealer trades.9 Withoutloss of generality the primary focus is on the bid side of the market,therefore, the superscript b or a is suppressed.In the tradition of Glosten and Milgrom (1985) and (Kyle 1985,

1989), customers are asymmetrically informed. With probability q; 0 q 1, a customer has private information about the value of the security.

7. With N f1; . . . ; ng representing the set of n dealers.8. The assumption of diverse values is justified by following Amihud and Mendelson

(1980), Ho and Stoll (1983), and Biais (1993) and assuming that risk-averse dealers havedifferent inventories and hence different expected values. Hansch et al. (1998) provide evi-dence that a dealers desire to sell is related to his relative inventory position. Although the riskaversion also affects the auction, these affects are ignored, following Biais (1993), as they areof second-order importance. The variable transaction costs may be order handling costs andsettlement and delivery costs. Fixed costs do not affect the value of a particular trade.9. See Wang and Viswanathan (2001) for a paper that focuses on interdealer trading.



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In the third stage, the revealed value of the security is either H or L. Theinformed customers know the true value in the first stage. Rational un-informed customer participation is motivated by a liquidity shock, riskaversion, or inventories different from dealers. Therefore, a dealer is will-ing to trade because the customer may be uninformed, but if the customeris informed, the dealer loses the difference between his bid and L or hisask and H.10 Uninformed customers have a quantity demand q. For sim-plicity, we assume uninformed customers demand the quoted depth,which is normalized to unity. Informed customers have infinite quantitydemands, because they have perfect information.11 Therefore, they tradeas much as they can with any dealer who has a quote better than the truevalue. While the assumption of infinite informed demand overempha-sizes the effect of adverse selection, it does not drive any results; the ef-fects are the same if dealers who post worse quotes have a lower chanceof trading with the informed customer.The dealers quote decisions are modeled as a first-price auction. This

basic structure captures the salient aspects of the dealer market. Quotesare formed by competing dealers, who take into account heterogeneousdealer inventories and costs, the level of competition, adverse selectionfrom informed customers, and as we will see, potential price improve-ments. The use of a first-price auction model results in quotes that are notconditioned on the simultaneous bids of other dealers. In a fragmentedmarket, such as a dealer market, price formation is characterized less byrepeated price increases that drive prices to the Bertrand equilibrium andmore by repeated quotes and trades. At eachmoment in time, dealers postquotes. A trade then either occurs or does not occur. Direct price com-petition is a characteristic of centralized or open outcry markets (such asthe Chicago options pit), where each agent knows that a trade is about tooccur and can call out a better price. In dealershipmarkets, dealers are notimmediately aware of the trades of other dealers. This is particularly truein a fast-moving market.12 This logic drives our decision to use a first-price auction.13 However, none of the normative predictions of the paperwould change under an English auction model. Thus, the papers resultsapply more generally to other types of markets.

10. For simplicity, we assume vb > L and va < H . This is logical, since L and H arecommon knowledge; therefore, dealers with values below L or above H could not except totrade and do not participate in the market.11. This is a simplification of the idea formalized by Easley and OHara (1987), that

informed traders prefer larger quantities.12. For a more compete discussion on the difference between a fragmented dealer market

and a centralized market, see Biais (1993).13. In a more dynamic setting, the market would be characterized through time as a re-

peated first-price (sealed-bid) auction, where in each auction, the values of the other dealersare unknown because recent trades are not in the other dealers information set. Furthermore,the values of every dealer change through time, due to information and the consummationof trades in the market.



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In the standard market-microstructure auction model with bidder het-erogeneity, such as Biais (1993), different dealers post different take-it-or-leave-it quotes, and customers then accept these quotes as fixed and decideto trade. In contrast to thesemodels, quotes in a dealershipmarket are oftenimproved. Thus, some prices are set by competitive bids and some are setby secondary interaction. In this way, this paper brings together some ofthe theories of Wolinsky (1990) and Biais (1993). It is an open questionas to who receives the improved prices and why they receive them.This paper considers two mechanisms through which some customers

receive improvements. In the first model, price improvements dependon the customers information; those customers who can demonstrateor commit to a lack of information receive improvements. In the secondmodel, improvements are based on the market power of the customer;some customers have the market power to negotiate an improvement. Theconsideration of a combination of a fragmented market, competition, anddifferent types of price improvement allows greater insights into the priceformation process.

A. Price Improvement Based on Customer Information

The most common theory of price improvement, first formalized bySeppi (1990) in the context of NYSE block trades, is that improvementsare given on the basis of customer information. With improvements, thetransaction is no longer anonymous; therefore, implicit contracts canbind repeat customers. The theory is straightforward: some customersrepeatedly interact with the dealers. When these customers are informedthey anonymously accept the quoted price, and when they are uninformedthey ask for an improvement.14 This equilibrium is enforced through apenalty technology employed by the dealer if he is hurt by the trade aftergiving an improvement.Barclay and Warner (1993) form and test a similar hypothesis. They

suggest that interaction allows the dealers to better assess the customersinformation. Uninformed traders, therefore, like to interact to convince thedealer that they are uninformed. If a customer cannot certify that he is un-informed, he does not receive an improvement and may even face a pricereduction. Therefore, informed customers trade anonymously at the quotes.We take the theories of Seppi (1990) and Barclay and Warner (1993)

as the basis for the model of improvements based on customer infor-mation.15 We assume that only a fraction of the customers have the

14. This idea is proposition 2 in Seppi (1990). More generally, customers can only im-perfectly signal that they are uninformed. The intuition of this paper does not depend on theperfect signal, although for tractability the signal is assumed to be perfect.15. Both hypotheses are further supported by evidence from Hansch et al. (1999), who find

evidence on the London exchange that is consistent with the hypothesis that customers havetrading relationships with dealers. And, they show that dealers make money on the small andlarge trades but losemoney onmedium-sized trades (trades that use all of the depth at the quote).



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relationship that allows them to interact with the dealer and commit to orreveal a lack of information. Furthermore, while only a fraction of thecustomers could receive an improvement, only the subset (1 q) of thatgroup who are actually uninformed do receive an improvement.The summation of model 1 is as follows. First, the dealers post quotes.

Second, a customer arrives. If the customer cannot interact with dealersand is uninformed, he trades 1 unit with the dealer posting the best quote.If the customer is informed, he trades 1 unit with every dealer. If thecustomer is uninformed and can interact with dealers then each dealermakes him another offer.16 This second offer is also modeled as a first-price auction.17 In the final stage, the true value is revealed.The dealers goal is to choose his quoted price and the amount of

price improvement to maximize profits. To trade with an uninformedcustomer who cannot receive an improvement, the dealer must offer thebest quote. To trade with a customer who can negotiate, the dealer mustoffer the best price-improved quote. Let b1i represent dealer is quotedbid, and b2i represent dealer is price-improved bid. In expectation, thedealer earns vi b1iProbb1i > b1j for all j 6 i if an uninformed cus-tomer who cannot interact with dealers arrives at the market. The dealerloses b1i L if an informed customer arrives at the market.18 And thedealer expects to earn vi b2iProbb2i > b2j for all j 6 i if an un-informed customer who can interact with dealers arrives at the market.Therefore, dealer is expected profit is

i 1 qavi b2iProbb2i > b2j for all j 6 i 1 q1 avi b1iProbb1i > b1j for all j 6 i qb1i L:

1To determine the probabilities of winning, assume that all bidders ex-cept bidder i use the conjectured invertible equilibrium bid functions,b1vj and b2vj (invertibility will be verified in equilibrium). There-fore, dealer i beats dealer j if b1i > b1vj or b2i > b2vj, depending onthe type of customer. Since the equilibrium bid functions are assumedto be invertible, these inequalities can be rewritten as b11 b1i > vj orb12 b2i > vj. Given the distribution of values, F(), the probability of

16. Since only uninformed customers ask for price improvements, the dealer faces noadverse selection from these customers. The dealers can therefore give better prices. Whetherthey choose to give price improvements depends on the competition in the market.17. We assume that the information from the first posting of quotes is still unknown to

the other dealers. However, this is not necessary for the results. The reader may prefer to thinkthat the quoted prices reveal the dealers information. In this case, the equilibrium best offerin the second round is the true value of the second-highest bidder. Thus, the release of infor-mation would change the model of competition for the uninformed customer to an English(ascending-bid) auction but would not change any of the results in the paper.18. No probability is associated with the loss, because the informed customers trade with

every dealer who quotes a price above the true value, L.



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i beating j is Fb11 b1i or Fb12 b2i, and the probability that dealeri beats all other dealers is Fn1b11 b1i or Fn1b12 b2i, since Fn1is the distribution function of the highest of n 1 draws from F().Therefore, dealer i chooses b1i and b2i to maximize expected profits:

maxb1i;b2i

i 1 qavi b2iFn1b12 b2i 1 q1 avi b1iFn1b11 b1i qb1i L: 2

Result 1. The unique symmetric equilibrium bid is

b1v vZ vv

Fn1xFn1v dx

" #1 a1 qFn1v

1 a1 qFn1v q

qL1 a1 qFn1v q ; 3

with equilibrium price improvement equal to b2v b1v =

vZ vv

Fn1xdxFn1v

" #"q

1 a1 qFn1v q

#

qL1 a1 qFn1v q 0; 4

and the price improved bid is equal to

b2v vZ vv

Fn1xdxFn1v

" #5

Proof. See the appendix.The dealers market bid is simply the weighted average of the deal-

ers optimal bid to the uninformed customers and the optimal bid tothe informed customers. More specifically, the dealers bid their value,v, minus a term because the competition is not perfect,

R vvFn1x=

Fn1vdx. This is the standard bid in a first price auction because vi R viv Fn1x=Fn1v is the expected value of the next-highest dealer

given that i has the highest value; the dealers bid to just beat the com-petition in expectation. However, v is the dealers value only if the cus-tomer is uninformed. Thus, the standard bid must be multiplied by theprobability that the customer is uninformed given that the customer isnot negotiating, 1 a1 qFn1v=1 a1 qFn1v q.If the customer is informed, then the dealers value is L. In this case, thecustomer trades with every dealer, so the level of competition is irrele-vant. Since L is the dealers value only if the customer is informed, it mustbe multiplied by the probability the customer is informed, given that the



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customer is not negotiating, q=1 a1 qFn1v q. And, b2(v)can be interpreted similarly; since improvements are given only to un-informed customers, the bid is just the optimal bid to an uninformed cus-tomer (multiplied by the probability that the customer is uninformed,given that the customer is uninformed, which is just 1). So the bids arejust the weighted averages of the optimal bids in each situation.19

The equilibrium asks, a1(v), can be found and interpreted similarly.The only differences are that the probability of winning is 1 Fvn1,and the informed customers value is H, and some signs are changed.Thus, a dealers quoted spread is a1v b1v.Note that, throughout this model, as in any standard information based

model, all of the market power is implicitly assumed to reside with thedealer, as each dealer posts take-it-or-leave-it offers. Dealers improve theprice only if competition forces them to do so. The model that followsallows for the possibility that customers can respond.Before analyzing the effects of price improvement, it is important to

first develop an alternative model of price improvement based on cus-tomers with the market power to negotiate improvements. This allows usto consider general effects of price improvement and determine whatdistinguishes the theories.

B. Price Improvement Driven by Customers with Market Power

An alternative theory of price improvement relaxes the assumption, im-plicit in the informationmodel, that the dealer has all themarket power andtherefore posts take-it-or-leave-it offers. The alternative theory assumesthat customers canmake counteroffers and negotiate with the dealers. Thisform of price improvement does not depend on the information of the cus-tomers. The theory simply assumes that customers have different amountsof market power and those customers with more market power negotiatebetter prices. Clearly, this market poweraffects price formation.The market power of customers arises from their large size, their

knowledge of markets, their technology, their low discount rates, andthe like. The negotiations literature has enumerated many potential reasonswhy customers could differ in their market power relative to the dealers.For simplicity we assume that the market power differences between

customers are such that only a fraction of customers can extract an im-provement. Furthermore, all negotiating customers have the samemarketpower relative to dealers. These negotiating customers are neither morenor less informed than customers who accept the quote.20 Since dealers

19. It is easily confirmed that, as long as q < 1, both bids are increasing in v, which wasassumed to start the problem. As long as some customers are not informed, q < 1, then thedealers can profit with a small enough quote, and those with higher values bid higher.20. For simplicity, we assume the probability of being informed, q, and the ability to

negotiate, a, are independent. As long as the correlation is the same across the models, it doesnot alter any normative conclusion.



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earn a profit from the customers that negotiate, we assume that dealerscannot commit ex ante not to negotiate. LetQb1 represent the outcomeof negotiations between a customer and a dealer who quotes a bid of b1in the market. For simplicity, we assume that the negotiation depend onlyon the quoted bid, which represents the dealers signal to the market abouthis desire to trade. Thus,Qb1 represents the price-improved quote. Thehat signifies the market power model; a distinction that is useful later. Wenow elaborate on Q().The summation of model 2 is as follows. First, the dealers post

quotes. Second, a customer arrives. If the customer is uninformed andcannot negotiate, he trades with the dealer who posts the highest quote.If the customer is uninformed and can negotiate, he trades with thedealer who provides the highest improved quote,Qb1. If the customeris informed, he trades with every dealer at a price of b1 or negotiateswith every dealer.21

A dealers goal is to choose his quoted price to maximize profits,accounting for the possibility of future negotiations. Since the negotia-tions depend on the marketwide quote and even the probability of nego-tiating with an uninformed customer depends on the marketwide quote,the dealer must account for the fact that his quote is influencing nego-tiations and the probability of negotiating with an uninformed customer.Let b1i represent dealer is quoted bid. In expectation the dealer earnsvi b1iProbb1i > b1j; for all j 6 i if an uninformed customer whocannot negotiate arrives at the market. The dealer loses b1i L orQb1i L if an informed customer arrives at the market, depending onwhether or not the customer can negotiate. And the dealer expects to earnvi Qb1iProbQb1i>Qb1j; for all j 6 i if an uninformed cus-tomer who can negotiate arrives at the market. Therefore, dealer is ex-pected profit is

maxb1i

i 1 qavi Qb1iProbQb1i > Qb1j; for all j 6 i

qaQb1i L 1 q1 avi b1i

Probb1i > b1j; for all j 6 i q1 ab1i L: 6

To determine the probabilities of winning, assume that all bidders ex-cept bidder i use the conjectured invertible equilibrium bid function,b1vj, and negotiations result in the conjectured invertible equilibrium,Q()(invertibility is verified in equilibrium). Therefore, dealer i beatsdealer j if b1i > b1vj or Qb1i > Qb1vj, depending on the typeof customer. Since the equilibrium bid functions are assumed to be

21. This overemphasizes the effect of information but is not important for the normativeconclusions.



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invertible, these inequalities can both be rewritten as b11 b1i > vj.Given the distribution of values, F(), the probability of i beating j isFb11 b1i, and the probability that dealer i beats all other dealers isFn1b11 b1i, since Fn1 is the distribution function of the highestof n 1 draws from F().Therefore, dealer i chooses b1i to maximize expected profits:

maxb1i

i 1 qavi Qb1iFn1b11 b1i qaQb1i L

1 q1 avi b1iFn1b11 b1i q1 ab1i L:7

To determine a closed-form solution, we must impose more structure onthe negotiation. The dealer and the customer bargainover money or, es-sentially, transferable utility. We assume that, if no trade occurs, the cus-tomer can get another dealer tomatch theBBO ( best bid or offer) so he cantrade at b1i. Thus, b1i is the disagreement outcome for the customer.The dealer must account for the fact that he could negotiate with an

informed customer. To negotiate with an uninformed customer, thedealer must have the highest Q(). Thus, the dealers expected value fora negotiated trade (and thus his highest willingness to pay) is a weightedaverage of vi and L:

vi1 qFn1b11 b1i qL1 qFn1b11 b1i q

V vi; b1i: 8

Therefore, if the dealer does not trade, he gets the same utility he wouldachieve from a trade at V vi; b1i. This defines his maximumwillingnessto pay.We assume that the customers beliefs about the dealers willingness

to pay defines the upper bound on the negotiation. This is the assump-tion that the dealer is signaling his interest in trade through the aggres-siveness of his quote. Given b1i customers believe that the dealer iswilling to pay V b11 b1i; b1i. In equilibrium, this is the dealers truewillingness to pay, but we assume that dealers believe that, out of equi-librium, negotiations still depend on the customers beliefs.22 There-fore, any negotiation results in the dealer paying b1i plus a fraction ofV b1

1b1i; b1i b1i.23

22. This simplification eliminates the possibility that alternate off-equilibrium-path beliefsabout the negotiation alter the equilibrium quotes. However, the normative conclusions aboutbargaining vs. information-based improvements still hold under many other reasonable off-equilibrium-path beliefs.23. Imposing the restriction that b1i plus a fraction of V b11 b1i; b1i b1i is less than

V v; b1i is logical, but this restriction never binds and does not affect the equilibrium.



#05507 UCP: JB article # 780402

For simplicity, we assume a reduced form for the negotiations. Nego-tiation results in the customer gaining a fraction b of the difference be-tween V b11 b1i; b1i and b1i.24 Thus,

Qb1i b1i bfV b11 b1i; b1i b1ig: 9This assumption covers a broad class of negotiationmodels and allows aclosed-form solution while providing excellent intuition about howcustomers with market power affect prices. In equilibrium, for example,this functional form encompasses the Nash (1950) bargaining solution.The Nash bargaining solution in this context provides each bargainerwith a disagreement utility and then the bargainers split the remainingutility equally. The quote Q()could also represent some form of repeatedgame such as a Rubienstein alternating-offers model.25 In either case, b,represents the relative bargaining power of the customers and dealers. Ifdealers aremore patient, more skillful, have lower negotiating costs or lowersearch costs, and so forth, then b is smaller and vice versa for customers.The dealers problem can now be rewritten as

maxb1i

ia 1 qvFn1b11 b1i qL1bb1Fn1b11 b1i1q

a 1 bb1q b 1 qb11 b1iFn1b11 b1i qL

1 a 1 q v b1

Fn1b11 b1i qb1 qL

: 10Results 2. If condition (A22) holds, then the unique symmetric equi-

librium bid is

b1v vZ vv

Fn1xFn1v1 ab dx

" #

1 qFn1v

1 qFn1v q qL

1 qFn1v q ; 11

24. Engelbrecht-Wiggins and Kahn (1991), RothKopf, Tiesberg, and Kahn (1991), andWaehrer (1999) all show that, if the information revealed by the bids in an auction is usedagainst the bidder, then a separating equilibrium in the auction may not exist. Waehrer (1999)seemsmost applicable, because he follows an auction by an alternating-offers bargainingmodeland shows that this eliminates separability. In each of these papers, the incentive compatibilityis violated because both the information is sure to be used and too much is taken from thebidder. In Katzman and Rhodes-Kropf (2001) information is revealed by the bids and thusbidders reduce their bids. However, if the impact of the information revelation on the bidder issmall, then a separating equilibrium is shown to exist. Therefore, in the model chosen here, thebargaining power of the customer must be low relative to the dealer or very few customers mustbe able to negotiate. The formal condition for this restriction is shown in eq. (A22).25. In a working paper by Bernhardt et al. (2002), the dealer weighs the value of maxi-

mizing his one-time revenue from the customer by not offering a price improvement againstthe future value of trades from offering present and future price improvements. In equilibrium,the dealer offers just enough price improvement to keep the trader from switching dealers.In the equilibrium of a dynamic model, b would be the amount that just keeps the customerfrom switching dealers.



#05507 UCP: JB article # 780402

with equilibrium price improvement equal to bfV v; b1v b1vg =

Qb1v b1v R vvFn1xdx1 q

1 ab1 qFn1v q

" #b 0; 12

and the price improved bid is equal to b1v bfV v; b1v b1vg =

Qb1v v1 qFn1v qL

1 qFn1v q 1 b R v

vFn1xdx1 q

1 ab1 qFn1v q : 13

Proof. See the appendix.This bid can be interpreted similarly to result 1, as a weighted average

dealers optimal bid to the uninformed customers and the optimal bidto the informed customers. However, the dealer must also account forimprovements when setting his bid. If no customer were informed andno customer could negotiate, then the optimal bid would be the standardfirst-price auction bid, v R v

vFn1x=Fn1vdx. If the customer is un-

informed and dealerwins the auction, 1 qFn1v, then the dealer paysthe customers bid; and if the customer can negotiate, then the dealerpays the customers bid plus the improvement. If these were the onlytwo possibilities, then the optimal bid would be the standard bid reducedby a term (1 ab) relating to the probability of negotiating, a, and thenegotiation power of the customer, b. However, the customer may be in-formed. In this case the dealer should bid L.The equilibrium ask, a1v, can be found and interpreted similarly.

Thus, a dealers quoted spread is a1v b1v.There are two key differences between the information-based model

of price improvement and the model based on customers with marketpower. The central difference, of course, is the information level of thecustomers who receive improvements. Customers who receive price im-provements in the information model have less information than theaverage customer who accepts the quoted price. However, in the market-power model, customers who negotiate are as informed on average asthe customers who accept the quoted price.This fundamental difference leads to the other key distinction in the

models: in the information model, the improved price does not dependon the quoted price, whereas in the market-power model we assume thatthe quoted price influences the negotiations. In the information model, acustomer cannot negotiate a better price simply because he is less in-formed; he receives a better price only because the dealers compete forhis uninformed trade. Therefore, the dealers quoted price does not in-fluence the improved price. In contrast, a customer with market powernegotiates directly with dealers. Since these customers are as informedas the average market participant, competition plays the same role that it



#05507 UCP: JB article # 780402

did in the original posting of quotes. Therefore, competition does not im-prove prices. However, negotiating power allows the customer to make acounteroffer and negotiate an improvement in spite of the lack of com-petition. Since the initial quote is the basis for negotiations, the initialquote influences the improved price.Thus, in the information model, the price to the uninformed customer

is higher because they are more valuable and there is competition amongdealers, but this price does not depend on the quoted price. In the market-power model, the negotiated price depends on the original quote and themarket power of the negotiator.This completes the basic outline of both models of price improvement.

The next section considers those aspects of price improvement that arefundamental and do not depend on how the improvements are determined.

III. Effects of Price Improvements

The two distinct notions of price improvements have different effects onthe trading participants. However, before examining their differences, itis important to establish those aspects of price improvement that areuniversal. This provides a framework to focus attention on the relevantdifferences between the two rationales for price improvements.In this section, the first theorem demonstrates the basic interaction

between information, the ability to negotiate, and the quoted prices inboth models. Then, the second theorem examines how the dealers ex-pected revenue is affected by the price improvements.Results 1 and 2 developed the dealers quotes and the quoted spread.

The prices most often examined are the best bid and ask, which are thesame prices quoted in the newspaper. The best bid or ask is the expectedhighest of n bids or the expected lowest of n asks. It is easy to see that theexpected highest bid (the first-order statistic) when improvements arebased on information is

b1v n

Z vv

vR vv

Fn1xFn1vdx

h i1 a1 qFn1v qL

1 a1 qFn1v q

F 0vFn1vdv; 14and the expected lowest ask, a1(v), is similar. The expected highest bidwhen improvements are based on market power is

b1v n

Z vv

v1 ab R vv

Fn1xFn1vdx

h i1 qFn1v q1 abL

1 ab1 qFn1v q

8 bb1x: A20



#05507 UCP: JB article # 780402

where 1 qvFn1v qL=1 qFn1v q is the dealers expected valuegiven that he is negotiating with the customer.31

This equilibrium is predicated on the assumption that the bid is invertible orincreasing in v and positive. As Waehrer (1999) points out, negotiation following anauction may eliminate an invertible equilibrium. The problem arises if, in expec-tation, the negotiation is able to extract too large a portion of the dealers surplus. Ifthe extraction is too large, then the dealers are better off pooling and hiding theirvalue. This alters the customers ability to extract the dealers surplus. To considerequilibria that are invertible, we must assume that expected extraction is not toolarge. Specifically, BB=BBvb1v > 0 requires

0 vR vv

Fn1xFn1v dx

h i1 EFn1v E1 abL abv1 EFn1v

1 abA sufficient condition is that

1 qvFn1v qL v1 qFn1v q1 abL abv1 qFn1v

1 abThis reduces to

1 qvFn1v EL v1 EFn1v qL:Therefore, the price improvement is positive.



#05507 UCP: JB article # 780402

If condition (A22) holds, then the bids are invertible and the dealers true value canbe determined by the negotiating customer. Furthermore, it is straightforward toshow that the negotiated outcome Q() is an increasing function of the bid and,therefore, also an increasing function of v. Throughout the paper, we assume thiscondition holds.

Proof of Theorem 1

The derivatives of the bid and the expected best bid with respect to the relevantvariable are

BBb1vBBa

n

Z vv

L vR vv

Fn1xFn1v dx

h in o1 qFn1vq

1 E1 qFn1v q2 F0vFn1vdv;

A23

BBb1vBBq

n

Z vv

L vR vv

Fn1xFn1v dx

h in o1 aFn1v

1 a1 qFn1v q2 F0vFn1vdv:

A24

Both derivatives are less than zero because v R vvFn1x=Fn1vdx > L. Then,

BBb1vBBa

nZ vv

bR vvFn1xdx1 q

f1 ab21 qFn1v qg

!F 0vFn1vdv; A25

which is less than zero. The derivative with respect to b, of course, also is less thanzero. Finally,

BBb1vBBq

nZ vv

v1 abFn1v R v

vFn1xdx

1 qFn1v q21 ab

( )F 0vFn1vdv; A26

which is negative, since condition (A22) holds, the bid is positive when q = 0, there-fore, v1 abFn1v R v

vFn1xdx > 0. The derivatives of the asks are not

shown but are similar. Q.E.D.

Proof of Theorem 2

In equilibrium, a dealers expected profit, when improvements are based on in-formation, is

v 1 qav b2vFn1v 1 q1 av b1vFn1v qb1v L: A27

Rearranging yields

v 1 qvFn1v b2v1 qaFn1v b1v1 q1 aFn1v q qL: A28



#05507 UCP: JB article # 780402

Substituting in the equilibrium bid function for b1v, equation (3), yieldsv 1 qvFn1v b2v1 qaFn1v

vZ vv

Fn1xFn1v dx

" #1 a1 qFn1v qL

( ) qL: A29

Substituting in the equilibrium bid function for b2(v), equation (5), yields

v Z vv

Fn1xdx1 q: A30

In equilibrium, a dealers expected profit when improvements are given becausecustomers have market power is

v v b1v abb1v abv1 qFn1v q1 abL b1v:A31

Rearranging yields

v 1 q1 abvFn1vb1v1 ab1 qFn1v q q1 abL: A32

Substituting in the equilibrium bid function for b1v, equation (11), yields

v Z vv

Fn1xdx1 q: A33

Note that equation (A30) equals equation (A33) and neither equation depends on aor b. Q.E.D.

Proof of Theorem 3

Examining the expected highest price-improved bid with information basedimprovements, b2(v), equation (16), it is immediately obvious that this price isnot affected by either a or q. However, the derivative of the expected highest price-improved bid when customers have market power, Qb1v, equation (17), withrespect to a is

BBQb1vBBa

nZ vv

1 bb R v

vFn1xdx1 q

f1 ab21 qFn1v qg F0vFn1vdv; A34

which is less than zero. The derivative of Qb1v with respect to q is

BBQb1vBBq

nZ vv

v1 abFn1v 1 E R v

vFn1xdx

1 qFn1v q1 ab1 qFn1v q F 0vFn1vdv; A35



#05507 UCP: JB article # 780402

which is negative, since condition (A22) holds. The bid is positive when q = 0;therefore, v1 abFn1v R v

vFn1xdx > 0, hence, v1 abFn1v

1 b R vvFn1xdx > 0. Q.E.D

Proof of Corollary 2

To see the transfer from the nonnegotiators to the negotiators, we need to look at theexpected payments to the groups.A customerwho can negotiate receives b2(v), from thedealer if the customer is uninformed and the price improvements are based on infor-mation, and Qb1v, if the improvements are due to market power. As a group, thosecustomers who negotiate expect to receive from a dealer the improved bids times theprobability that the customer negotiates times the probability that dealer wins (which isa1 qFn1v if improvements are information based, since the negotiator must beuninformed, and just a1 qFn1v q if the improvements are due to marketpower). Therefore, the change in the negotiating groups profit with a change in a is

BB

BBanEa1 qFn1vb2v

nZ vv

1 qFn1v vZ vv

Fn1xdxFn1v

" #F 0vFn1vdv; A36

if improvements are based on information. And the change in the negotiating groupsprofit with a change in a is

BB

BBanE aQb1v1 qFn1v qn o

nZ vv

v1 qFn1v qL1 b R v

vFn1xdx1 q

1 ab2" #

F 0vFn1vdv;A37

pay 1 a1 qFn1vb1v qb1v, given their v, to those customers whomust accept the inside spread. Since there are n dealers, the total expected payment tothe group that cannot negotiate is

nE1a1 qFn1vb1v qb1v or nE1 ab1v1 qFn1v qg;A38

depending on the type of improvements in the market. The derivatives of eachgroups profit with respect to a is

BB

BBanEf1 a1 qFn1v qb1vg

nZ vv

1 qFn1v vZ vv

Fn1xFn1v dx

" #F 0vFn1vdv; A39

BB

BBa1 ab1v1 qFn1v qn o

nZ vv

v1 qFn1v qL1 b R v

vFn1xdx1 q

1 ab2" #

F 0vFn1vdv:A40



#05507 UCP: JB article # 780402

Since

BB

BBanEa1 qFn1vb2v BB

BBanEf1 a1 qFn1v qb1vg

A41and

BB

BBaaQb1v1 qFn1v qn o

BBBBa

1 ab1v1 qFn1v qn o

;

A42then as the probability of negotiation increases from zero, the benefit to the ne-gotiating group is exactly offset by the reduction to the nonnegotiators.32 Q.E.D.

Proof of Theorem 4

The price improvement with information-based improvements is

b2v b1v vR vv

Fn1xFn1v dx

h iq qL

1 a1 qFn1v q : A43

This is clearly increasing, since the numerator is increasing and the denominator isdecreasing with n.The price improvement with market-power-based improvementsis

Qb1v b1v R vvFn1xdx1 q

1 ab1 qFn1v q

( )b: A44

The derivative of the numerator with respect to n isR vvFn1xlnFn1xdx1 q

1 ab1 qFn1v q

R vvFn1xdx1 q ln Fn1v

f1 ab1 qFn1v qg2 1 ab1 qFn1v: A45

Further,Z vv

Fn1xln Fn1xdx Z vv

Fn1x ln Fn1xdx: A47

Therefore, the improvement decreases when n increases. Q.E.D.

32. The same is true for the market power of negotiators.



#05507 UCP: JB article # 780402

If @ Depends on the Bid

The bid in the market-power game is a function of v and the parameters q;a; b; Land n : b1 hv; q;a; b; L; n. It is easy to demonstrate that, if b is a function of thebid, then the bid can be defined by the implicit function b1 hv; q;a; bb1; L; n,as long as condition (A22) with bb1is still assumed to hold. Using this implicitfunction and the preceding proofs, we can show that the theorems are unchanged,as long as BBbb1=BBb1 is not too small.

For example, the derivative of the bid function with respect to a is

BBb1

BBa h3v; q;a; bb1; L; n h4v; q;a; bb1; L; n BBbb1

BBb1

BBb1BBa

; A48

where the subscript represents the derivative with respect to the nth argument:

BBb1

BBa h3v; q;a; bb1; L; n

1 h4v; q;a; bb1; L; nBbb1Bb1

: A49

Thus, the effect of a change in a has the same sign as for a fixed b as long as

1 h4v; q;a; bb1; L; n BBbb1BBb1

> 0: A50

Note 29 demonstrates that the derivative of the old bid function with respect to b isnegative h4v; q;a; bb1; L < 0. Therefore, as long as BBbb1=BBb1 is positive ornot too negative,

BBbb1BBb1

>1

h4v; q;a; bb1; L; A51

Then the effect of a change in a (or a change in q) has the same sign as before, sotheorems 1 and 3 hold. The same logic can be used on equation (A44) to demon-strate theorem 4 is true as long as condition (A51) holds. Theorem 2 is unchanged.

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