This note considers a bargaining environment with two-sided asymmetric information and quasilinear preferences in which parties select bargaining mechanism after learning their valuations. I demonstrate that sometimes the buyer achieves a higher ex-ante payoff if the bargaining mechanism is selected by her opponent rather than by herself. In the model, the buyer has limited wealth and in addition to acquiring one good from the seller can purchase a different good from a competitive market. The positive relation between the values of these goods is what delivers our result

Mylovanov, Tymofiy

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Sonderforschungsbereich/Transregio 15 · www.gesy.uni-mannheim.de Universität Mannheim · Freie Universität Berlin · Humboldt-Universität zu Berlin · Ludwig-Maximilians-Universität München Rheinische Friedrich-Wilhelms-Universität Bonn · Zentrum für Europäische Wirtschaftsforschung Mannheim  Speaker: Prof. Konrad Stahl, Ph.D. · Department of Economics · University of Mannheim · D-68131 Mannheim, Phone: +49(0621)1812786 · Fax: +49(0621)1812785                      October 2005   *Tymofiy Mylovanov, Department of Economics, University of Bonn, Adenauerallee 24-42, 53113 Bonn. mylovanov@uni-bonn.de    Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged. Discussion Paper No. 127 First-mover disadvantage Tymofiy Mylovanov* First-mover disadvantage.∗Tymofiy Mylovanov †October 31, 2005AbstractThis note considers a bargaining environment with two-sided asymmetricinformation and quasilinear preferences in which parties select bargaining mech-anism after learning their valuations. I demonstrate that sometimes the buyerachieves a higher ex-ante payoff if the bargaining mechanism is selected by heropponent rather than by herself. In the model, the buyer has limited wealthand in addition to acquiring one good from the seller can purchase a differentgood from a competitive market. The positive relation between the values ofthese goods is what delivers our result.JEL Codes: C72, C78, D82.This note presents a simple bargaining model with two-sided asymmetric informa-tion and quasilinear preferences, in which the buyer selects a bargaining mechanismafter learning her valuation.1 I demonstrate that there exist circumstances such thatthe buyer achieves a higher ex-ante payoff if the mechanism is selected by her oppo-nent rather than by herself.In my model, in addition to acquiring one good from the seller, the buyer can alsoacquire some other good, whose value is positively related to the (relative) value ofthe first good. Because the buyer has limited wealth and uses the monetary rentsremaining after bargaining with the seller to purchase the other good, her ex-antepayoff is maximized in a mechanism that generates relatively high monetary rents forthe types with high valuations and zero payoffs for the types with low valuations.However, if the buyer selects a mechanism after learning her valuation, the typeswith low valuations can always achieve some positive payoff by offering an ultimatumbargaining game; this makes impossible for the buyer to implement an ex-ante optimal∗This note is based on my dissertation, submitted to the Graduate School of the Universityof Wisconsin - Madison. I would like to thank my advisor Larry Samuelson for his continuousencouragement and support. I am also grateful to James Andreoni, Bart Lipman, Lucia Quesada,Bill Sandholm, and especially Patrick Schmitz for discussions and suggestions. Financial supportfrom the project SFB 15, Projektbereich A is gratefully acknowledged.†Department of Economics, University of Bonn, Adenauerallee 24-42, 53113 Bonn.Email:mylovanov@uni-bonn.de1That is, the buyer is an informed principal. Myerson [10] and Maskin and Tirole [8] and [9] arethe main references in this field.1mechanism. Results in Yilankaya [18] imply that in this environment all types ofthe buyer will always implement an allocation that is equivalent to the equilibriumallocation of the ultimatum bargaining game conditional on their type.2 (A symmetricresult holds if the seller selects a mechanism.)Now imagine that instead of the buyer, the mechanism is chosen by the seller.The seller will select an ultimatum bargaining game, in which she makes a take-it-or-leave-it price offer. The seller will extract almost all valuation from mediumvaluation types, exclude from trade low valuation types, and leave some rent to thehigh valuation types of the buyer. Importantly, the expected rents for the high typesof the buyer could be quite large resulting in a bigger ex-ante payoff in this gamethan in the ultimatum game in which the buyer makes an offer herself.The fact that because of the conflict of preferences among different types of aplayer, the allocation implemented by her types does not maximize her ex-ante payoffis not specific to my model. (Mylovanov [13] demonstrates that for generic prior beliefsand concave payoffs a player who is privately informed will fail to implement ex-anteoptimal allocation.) This note shows that this conflict could be so destructive thatthe implemented allocation is ex-ante inferior to the allocation that maximizes the(ex-ante and interim) payoff of the opponent and ignores the payoff of the player.3Environment. There is a buyer who can purchase two goods A and B. Good Acan only be acquired from a seller, who has one unit of this good. The seller’s costc of good A is her private information. Good B can be acquired from a competitivemarket with unlimited supply at the unit price normalized to one. The buyer’s hastotal wealth of W > 1 (With unlimited wealth, the buyer in my model would acquireinfinite amount of good B).The marginal values of the goods A and B for the buyer are correspondingly vAand vB.4 In order to make purchase of good B always desirable, it is assumed thatvB ≥ 1. Let v = vA/vB be the relative value of good A. I assume that v uniquelydetermines values vA and vB and, in particular, that vB = g(v), where g(·) is a weaklyincreasing function. This relative value v is (one-dimensional) private information ofthe buyer. The seller’s and the buyer’s private information (types), c and v, aredistributed according to Fc(·) and Fv(·) with continuous differentiable bounded andeverywhere strictly positive densities fc(·) and fv(·) and support on [0, 1].Let x be the exchanged amount of good A and p be the price paid by the buyerto the seller. Then, the payoff of the seller is us(c, x, p) = p − xc and the payoff ofthe buyer is ub(v, x, p) = xvA + vB(W − p) = vB(x vAvB +W − p) = g(v)(xv +W − p).Notice that the buyer’s interim preferences can be represented by a function which2In this note, equivalence is meant in terms of the parties’ expected payoffs conditional on theirprivate information. Yilankaya [18] has proven the result that the informed seller will implement anallocation equivalent to the equilibrium allocation of the ultimatum bargaining game. It is immediateto modify his arguments to establish the result for the buyer.3Unlike the buyer, the seller in my model would implement the same allocation regardless ofwhether she selects a mechanism ex-ante or after learning her type.4An alternative interpretation is to think of goods A and B as intermediate goods in productionof a final good Y whose value is 1 and whose production technology is given by Y = vAxA + vBxB ,where xA, xB , and Y are the corresponding amounts of the goods.2measures the monetary surplus from trade in good A, u˜b(v, x, p) = xv − p.5 Hence,after the parties’ private information has been realized, this environment becomesequivalent to the bargaining setting with two-sided incomplete information in Myersonand Satterthwaite [11].Bargaining. When the buyer selects a mechanism, the timing of the game is asfollows: First, the parties simultaneously and privately observe their own types. Then,the buyer offers a mechanism. If the seller accepts, the mechanism is played and thebuyer pays the price and obtains the amount of good A prescribed by the mechanism.After that, the buyer acquires good B from the market.6 The game ends. When theseller selects a mechanism, the roles are reversed: the seller makes a mechanism offerand the buyer decides whether to accept it. The rest of the game is the same asbefore. The solution concept for these games is Perfect Bayesian equilibrium.7Mechanism selection. Because at the moment of mechanism selection, the prefer-ences of the players can be described by us(c, x, p) = p− xc and u˜b(v, x, p) = xv − p,the results in Yilankaya [18] are valid for my setting. Yilankaya shows that the sellerwho has private information about her valuation at the moment of selecting a mech-anism will implement an allocation equivalent to the allocation resulting from theultimatum bargaining game.8 Similar results are straightforward to obtain for thebuyer.Result. Notice that the ex-ante payoff of the buyer can be written as∫ 10g(v)(U˜(v)+W )fv(v)dv, where U˜(v) = Eu˜b(v, x, p). Let us denote by U˜S(v) and U˜B(v) the buyer’sexpected payoff conditional on her type in the mechanism selected by the seller andthe mechanism selected by the buyer correspondingly. If g(v) is relatively high forlarge v and for the high types of the buyer U˜S(v) > U˜B(v), the buyer’s ex-ante payoffis higher in the game where she receives an ultimatum offer:Proposition 1. If there is some v′ < 1 such that U˜S(v) > U˜B(v) for all v > v′, thenthere exists g(·) for which the ex-ante expected payoff of the buyer is strictly higher ifthe mechanism is selected by her opponent rather than by herself.Proof. The difference between the ex-ante expected payoffs in the game where the5After the private information of the buyer is realized, she treats g(v) as a constant. Then, onecan divide ub(v, x, p) by g(v) and subtract W to obtain u˜b(v, x, p).6In the model, there are three endogenously determined variables: the payment for good A andthe amounts of goods A and B acquired by the buyer. It is assumed that the parties can contractonly on the first two.7For a precise description of mechanism selection game, including the set of allowed mechanismsand details of the solution concept see Maskin and Tirole [9] and Mylovanov [12].8Yilankaya invokes the characterization of an ex-ante optimal allocation in Williams [17], whichrequires additional assumptions on distribution functions, e.g., monotonicity of the hazard rate of thebuyer’s distribution. Proposition 2 in Mylovanov [12] extends Yilankaya’s result to non-monotoniccase.3seller sets the price and the buyer sets the price is∆ =∫ 10g(v)(U˜S(v)− U˜B(v))fv(v)dv =∫ v′0g(v)(U˜S(v)− U˜B(v))fv(v)dv+∫ 1v′g(v)(U˜S(v)− U˜B(v))fv(v)dv.It is immediate that there exist g(·) increasing on [v′, 1] such that the second termin the above expression is large enough to ensure ∆ > 0.Example. Let Fc(c) = c and Fv(v) = 1−(1−v)4. Then, it is direct to demonstratethat there exists v′ ≈ 0.544 such that U˜S(v) ≥ U˜B(v) if v ≥ v′ and U˜S(v) < U˜B(v)otherwise. If g(v) = 1 + 3v, the buyer’s ex-ante payoff is higher in the game whereher opponent selects the mechanism.First-mover disadvantage. The result in Proposition 1 can be equivalently statedas that the buyer may have first-mover disadvantage in the ultimatum bargaininggame: she obtains a higher ex-ante payoff in the game in which she moves secondreceiving an ultimatum price offer than in the game in which she moves first makingsuch an offer herself.9 This is in accordance with some of the business bargainingliterature which recommends to wait for an offer rather than to make one.10Li and Tan [6] make a similar observation in the context of a choice between hiddenand announced reserve price in auctions with risk-averse bidders and continuous types.In one-bidder environment announcing the reservation price is equivalent to makinga take-it-or-leave-it price offer, whereas hiding the reservation price is equivalent toreceiving such an offer. Li and Tan show that a sufficiently risk-averse bidder willmake offers which are very close to her true valuation and therefore receiving anoffer generates a higher ex-ante payoff for the seller than making an offer. My modeldiffers in two important respects. First, it is currently not known which mechanismwill be selected by the informed seller in the environment in Li and Tan. However, theresults in Quesada [15] suggest that the seller will offer a mechanism that is differentfrom and achieves a higher expected payoff than in the ultimatum bargaining game.11Furthermore, in my model there is no risk-aversion.9First-mover disadvantage is often present in Bertrand duopoly games due to ability to undercutthe first mover and in Cournot duopoly games with incomplete information due to the distortion inthe equilibrium action caused by signalling effects (Dowrick [3], Gal-Or [4], Amir and Stepanova [1],Mailath [7], Normann [14]). In the models of research and development and adoption of new tech-nology, a second-mover advantage may appear because of informational spillovers or technologicaladvances Reinganum [16] and Hoppe and Lehmann-Grube [5].10See, for instance “The Sourcing Solution: A Step-By-Step Guide to Creating a Successful Pur-chasing Program,” by Larry Paquette, p. 147, “Flipping Properties: Generate Instant Cash Profitsin Real Estate,” by William Bronchick and Robert Dahlstrom, p. 66, “On-Scene Guide for CrisisNegotiators,” by Frederick J. Lanceley, p. 90, “Energy Economics and International Energy Mar-kets,” by Carol A Dahl, p. 245, “From the Complete Idiot’s Guy to Getting Along with DifficultPeople,” by Brandon Toropov, p. 191.11Quesada considers a setting with discrete types and one risk-averse agent. It is simple to show4Finally, Cornet [2] presents a bargaining model in which there is a seller and twobuyers, who can resell the good to each other. The possibility of resale increasescompetition among the buyers and may lead to a higher ex-ante payoff for the sellerin the game where she receives the buyers’ offers than in the game where she makesan offer herself.References[1] Rabah Amir and Anna Stepanova, First and second mover advantage in asym-metric proce duopoly, Games and Economic Behavior, forthcoming.[2] Maarten Cornet, Externalities in a bargaining model of public price announce-ments and resale, Theory and Decision 49 (2000), 375–93.[3] Steve Dowrick, von Stackelberg and Cournot duopoly: Choosing roles, RANDJournal of Economics 17 (1986), no. 2, 251–60.[4] Esther Gal-Or, First mover and second mover advantages, International Eco-nomic Review 26 (1985), no. 3, 649–53.[5] Heidrun C. Hoppe and Ulrich Lehmann-Grube, Innovation timing games: ageneral framework with applications, Journal of Economic Theory 121 (2005).[6] Huagang Li and Guofu Tan, Hidden reserve prices with risk-averse bidders, Uni-versity of Southern California, 2000.[7] George J. Mailath, Endogenous sequencing of firm decisions, Journal of EconomicTheory 59 (1993), no. 1, 169–82.[8] Eric Maskin and Jean Tirole, The principal-agent relationship with an informedprincipal, II: Common values, Econometrica 58 (1990), no. 2, 379–409.[9] , The principal-agent relationship with an informed principal: The caseof private values, Econometrica 58 (1990), no. 2, 379–409.[10] Roger B. Myerson, Mechanism design by an informed principal, Econometrica51 (1983), no. 6, 1767–1798.[11] Roger B. Myerson and Mark A. Satterthwaite, Efficient mechanisms for bilateraltrading, Journal of economic theory 29 (1983), no. 2, 265–281.[12] Tymofiy Mylovanov, The informed principal problem with independent privatevalues and quasilinear preferences, University of Bonn, 2005.that in her environment the equilibrium allocation in the ultimatum bargaining game is independentof the risk attitude of the agent. On the other hand, Quesada shows that the allocation implementedby the informed seller depends on the risk attitudes of the agent and hence is different. Because theseller can always implement the allocation of the ultimatum bargaining game, in the equilibrium allher types must be achieving a higher payoff.5[13] , Negative value of information in the informed principal problem withindependent private values, University of Bonn, 2005.[14] Hans-Theo Normann, Endogenous timing with incomplete information and withobservable delay, Games and Economic Behavior 39 (2002), 282–91.[15] Lucia Quesada, Informed principal in the private values framework: A simplifiedanalysis, University of Wisconsin-Madison, 2002.[16] Jennifer F. Reinganum, A two-stage model of research and development withendogenous second-mover advantages, International Journal of Industrial Orga-nization 3 (1985), no. 3, 275–92.[17] Steven R. Williams, Efficient performance in two-agent bargaining, Journal ofeconomic theory 41 (1987), no. 1, 154–172.[18] Okan Yilankaya, A note on the seller’s optimal mechanism in bilateral trade withtwo-sided incomplete information, Journal of Economic Theory 87 (1999), no. 1,125–143.6

A note on the seller's optimal mechanism in bilateral trade with two-sided incomplete information,

A two-stage model of research and development with endogenous second-mover advantages,

E±cient mechanisms for bilateral trading,

E±cient performance in two-agent bargaining,

Endogenous sequencing of ¯rm decisions,

Endogenous timing with incomplete information and with observable delay,

Externalities in a bargaining model of public price announcements and resale,

First and second mover advantage in asymmetric proce duopoly,

First mover and second mover advantages,

Hidden reserve prices with risk-averse bidders,

Informed principal in the private values framework: A simpli¯ed analysis,

Innovation timing games: a general framework with applications,

Mechanism design by an informed principal,

The informed principal problem with independent private values and quasilinear preferences,

The principal-agent relationship with an informed principal, II: Common values,

The principal-agent relationship with an informed principal: The case of private values,

von Stackelberg and Cournot duopoly: Choosing roles,

First-mover disadvantage

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First-mover disadvantage

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