
on Game Theory 
Issue of 2012‒12‒06
fourteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Andrew Monaco (Department of Economics, Colgate University); Tarun Sabarwal (Department of Economics, University of Kansas) 
Abstract:  This paper studies games with both strategic substitutes and strategic complements, and more generally, games with strategic heterogeneity (GSH). Such games may behave differ ently from either games with strategic complements or games with strategic substitutes. Under mild assumptions (on one or two players only), the equilibrium set in a GSH is totally unordered (no two equilibria are comparable in the standard product order). Moreover, under mild assumptions (on one player only), parameterized GSH do not allow decreasing equilibrium selections. In general, this cannot be strengthened to conclude in creasing selections. Monotone comparative statics results are presented for games in which some players exhibit strategic substitutes and others exhibit strategic complements. For twoplayer games with linearly ordered strategy spaces, there is a characterization. More generally, there are sufficient conditions. The conditions apply only to players exhibiting strategic substitutes; no conditions are needed for players with strategic complements. Several examples highlight the results. 
Keywords:  Lattice games, strategic complements, strategic substitutes, strategic hetergeneity, equilibrium set, monotone comparative statics 
JEL:  C70 C72 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:kan:wpaper:201240&r=gth 
By:  Rida Laraki (Ecole Polytechnique  Ecole Polytechnique, IMJ  Institut de Mathématiques de Jussieu  CNRS : UMR7586  Université Paris VI  Pierre et Marie Curie  Université Paris VII  Paris Diderot); Eilon Solan (School of Mathematical Sciences [Tel Aviv]  Raymond and Beverly Sackler Faculty of Exact Sciences) 
Abstract:  We prove that every twoplayer nonzerosum Dynkin game in continuous time admits an "epsilon" equilibrium in randomized stopping times. We provide a condition that ensures the existence of an "epsilon" equilibrium in nonrandomized stopping times. 
Keywords:  Dynkin games, stopping games, equilibrium, stochastic analysis, continuous time. 
Date:  2012–11–19 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal00753508&r=gth 
By:  Laruelle, Annick; Iñarra García, María Elena; Zuazo Garín, Peio 
Abstract:  We assume that 2 x 2 matrix games are publicly known and that players perceive a dichotomous characteristic on their opponents which defines two types for each player. In turn, each type has beliefs concerning her opponent's types, and payoffs are assumed to be typeindependent. We analyze whether the mere possibility of different types playing different strategies generates discriminatory equilibria. Given a specific information structure we find that in equilibrium a player discriminates between her types if and only if her opponent does so. We also find that for dominant solvable 2x2 games no discriminatory equilibrium exists, while under different conditions of concordance between players' beliefs discrimination appears for coordination and for competitive games. A complete characterization of the set of Bayesian equilibria is provided. 
Keywords:  incomplete information, 2x2 matrix games 
JEL:  C72 
Date:  2012–10–23 
URL:  http://d.repec.org/n?u=RePEc:ehu:ikerla:9099&r=gth 
By:  Yuichi Yamamoto (Department of Economics, University of Pennsylvania) 
Abstract:  We investigate whether two players in a longrun relationship can maintain cooperation when the details of the underlying game are unknown. Specifically, we consider a new class of repeated games with private monitoring, where an unobservable state of the world influences the payoff functions and/or the monitoring structure. Each player privately learns the state over time, but cannot observe what the opponent learns. We show that there are robust equilibria where players eventually obtain payoffs as if the true state were common knowledge and players played a “belieffree” equilibrium. The result is applied to various examples, including secret pricecutting with unknown demand. 
Keywords:  repeated game, private monitoring, incomplete information, belieffree equilibrium, expost equilibrium, individual learning 
JEL:  C72 C73 
Date:  2012–11–10 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:12044&r=gth 
By:  Jeanne Hagenbach (Department of Economics, Ecole Polytechnique  CNRS : UMR7176  Polytechnique  X); Frédéric Koessler (PSE  ParisJourdan Sciences Economiques  CNRS : UMR8545  Ecole des Hautes Etudes en Sciences Sociales (EHESS)  Ecole des Ponts ParisTech  Ecole Normale Supérieure de Paris  ENS Paris); Eduardo PerezRichet (Department of Economics, Ecole Polytechnique  CNRS : UMR7176  Polytechnique  X) 
Abstract:  This article asks when communication with certi able information leads to complete information sharing. We consider Bayesian games augmented by a preplay communication phase in which announcements are made publicly. We characterize the augmented games in which there exists a full disclosure sequential equilibrium with extremal beliefs (i.e., any deviation is attributed to a single type of the deviator). This characterization enables us to provide di erent sets of su cient conditions for full information disclosure that encompass and extend all known results in the literature, and are easily applicable. We use these conditions to obtain new insights in sendersreceiver games, games with strategic complementarities, and voting with deliberation. 
Keywords:  Strategic Communication; Hard Information; Information Disclosure; Masquerade Relation; Belief Consistency; Single Crossing Di erences; Supermodular Games 
Date:  2012–11–19 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:hal00753473&r=gth 
By:  Nejat Anbarci; Chingjen Sun 
Abstract:  This article proposes a simple Nash program. Both our axiomatic characterization and our noncooperative procedure consider each distinct asymmetric and symmetric Nash solution. Our noncooperative procedure is a generalization of the simplest known sequential Nash demand game analyzed by Rubinstein, Safra and Thomson (1992). We then provide the simplest known axiomatic characterization of the class of asymmetric Nash solutions, in which we use only Nash’s crucial Independence of Irrelevant Alternatives axiom and an asymmetric modification of the wellknown Midpoint Domination axiom. 
Keywords:  Asymmetric Nash bargaining solutions, Nash program, axiomatic characterization, noncooperative foundations, economics of search. 
JEL:  C78 D74 
Date:  2012–11–17 
URL:  http://d.repec.org/n?u=RePEc:dkn:econwp:eco_2012_9&r=gth 
By:  Normann, HansTheo; Rösch, Jürgen; Schultz, Luis Manuel 
Abstract:  We explore whether buyer groups, in which firms legally purchase inputs jointly, facilitate collusion in the product market. In a repeated game, abandoning the buyer group altogether or excluding single firms from them constitute more severe credible threats, hence, in theory buyer groups facilitate collusion. We run several experimental treatments in a threefirm Cournot framework to test these predictions, and we also explore the impact communication has on buyer groups. The experimental results show that buyer groups lead to lower outputs when groups can exclude single firms. Communication is identified as a main factor causing collusive product markets.  
Keywords:  buyer groups,cartels,collusion,communication,experiments,repeated games 
JEL:  C7 C9 L4 L41 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:zbw:dicedp:74&r=gth 
By:  Nejat Anbarci; Nick Feltovich 
Abstract:  Previous research has shown that individuals do not respond to changes in their bargaining position to the extent predicted by standard bargaining theories. Most of these results have come from experiments with bargaining power allocated exogenously, so that individuals may perceive it as having been “unearned” and thus be reluctant to exploit it. Also, equal splits of the “cake” (the amount bargained over) have typically been equilibrium outcomes, leading to a powerful tendency toward 5050 splits. We conduct a bargaining experiment in which subjects earn their bargaining power through a real–effort task. Treatments are based on the Nash demand game (NDG) and a related unstructured bargaining game (UBG). Subjects bargain over a fixed amount of money, with disagreement payments determined entirely by the number of units of the real–effort task successfully completed. Task parameters are set to allow disagreement payoffs above half the cake size, in which case 50–50 splits are not individually rational, and thus not consistent with equilibrium. We find that subjects are least responsive to changes in own and opponent disagreement payoffs in the NDG with both disagreement payments below half the cake size. Responsiveness is higher in the UBG, and in the NDG when one disagreement payment is more than half the cake size, but in both cases it is still less than predicted. It is only in the UBG when a disagreement payment is more than half the cake size that responsiveness to disagreement payoffs reaches the predicted level. Our results imply that even when real–life bargaining position is determined by past behaviour rather than luck, the extent to which actual bargaining corresponds to theoretical predictions will depend on (1) the institutions within which bargaining takes place, and (2) the distribution of bargaining power; in particular, whether the 50–50 norm yields a viable outcome. 
Keywords:  Nash demand game, unstructured bargaining, real effort, disagreement, experiment. 
JEL:  C78 C72 D81 
Date:  2012–11–16 
URL:  http://d.repec.org/n?u=RePEc:dkn:econwp:eco_2012_6&r=gth 
By:  Andrea Gallice (Department of Economics and Statistics (Dipartimento di Scienze EconomicoSociali e MatematicoStatistiche), University of Torino, Italy) 
Abstract:  A price reveal auction is a Dutch auction in which the current price of the item on sale remains hidden. Bidders can privately observe the price only by paying a fee, and every time a bidder does so, the price falls by a predetermined amount. We solve for the perfect Bayesian equilibria of the game. If the number of participants n is common knowledge, then in equilibrium at most one bidder observes the price and the profits that the mechanism raises, if any, are only marginally higher than those that would stem from a normal sale. If instead n is a random variable then multiple entry can occur and profitability is enhanced. 
Keywords:  payperbid auctions, endogenous price decrease 
JEL:  C72 D44 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:tur:wpapnw:015&r=gth 
By:  Nejat Anbarci; Chingjen Sun 
Abstract:  Most reallife bargaining is resolved gradually. During this process parties reach intermediate agreements. These intermediate agreements serve as disagreement points in subsequent rounds. We identify robustness criteria which are satisfied by three prominent bargaining solutions, the Nash, Proportional (and as a special case to the Egalitarian solution) and Discrete Raiffa solutions. We show that the .robustness of intermediate agreements. plus additional wellknown and plausible axioms, provide novel axiomatizations of the abovementioned solutions. Hence, we provide a unified framework for comparing these solutions’ bargaining theories. 
Keywords:  Nash’s bargaining problem, robustness, intermediate agreements, the Discrete Raiffa solution, the Nash solution, Proportional solutions. 
JEL:  C78 D74 
Date:  2012–11–16 
URL:  http://d.repec.org/n?u=RePEc:dkn:econwp:eco_2012_7&r=gth 
By:  Xu, Yongsheng; Yoshihara, Naoki 
Abstract:  Conditions α and β are two wellknown rationality conditions in the theory of rational choice. This paper examines the implications of weaker versions of these two rationality conditions in the context of solutions to nonconvex bargaining problems. It is shown that, together with the standard axioms of efficiency and strict individual rationality, they imply rationalizability of solutions to nonconvex bargaining problems. We then characterize asymmetric Nash solutions by imposing a continuity and the scale invariance requirements. These results make a further connection between solutions to nonconvex bargaining problems and rationalizability of choice function in the theory of rational choice. 
JEL:  C71 C78 D63 D71 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:hit:hituec:580&r=gth 
By:  Peter A. Streufert (University of Western Ontario) 
Abstract:  We introduce three definitions. First, we let a "basement" be a set of nodes and actions that supports at least one assessment. Second, we derive from an arbitrary basement its implied "plausibility" (i.e. infiniterelativelikelihood) relation among the game's nodes. Third, we say that this plausibility relation is "additive" if it has a completion represented by the nodal sums of a mass function defined over the game's actions. This last construction is built upon Streufert (2012)'s result that nodes can be specified as sets of actions. Our central result is that a basement has additive plausibility if and only if it supports at least one consistent assessment. The result's proof parallels the early foundations of probability theory and requires only Farkas' Lemma. The result leads to related characterizations, to an easily tested necessary condition for consistency, and to the repair of a nontrivial gap in a proof of Kreps and Wilson (1982). 
Keywords:  plausibility relation;additive representation; plausibility mass function; infinite relative likelihood 
JEL:  C72 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:uwo:uwowop:20123&r=gth 
By:  Holmberg, P.; Willems, Bert (Tilburg University, Center for Economic Research) 
Abstract:  Abstract: We demonstrate how suppliers can take strategic speculative positions in derivatives markets to soften competition in the spot market. In our game, suppliers first choose a portfolio of call options and then compete with supply functions. In equilibrium firms sell forward contracts and buy call options to commit to downward sloping supply functions. Although this strategy is risky, it reduces the elasticity of the residual demand of competitors, who increase their markups in response. We show that this type of strategic speculation increases the level and volatility of commodity prices and decreases welfare. 
Keywords:  Supply function equilibrium;Option contracts;Strategic commitment;Speculation. 
JEL:  C73 D43 D44 G13 L13 L94 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:2012088&r=gth 
By:  Bettina Klose; Paul Schweinzer 
Abstract:  We develop the idea of using meanvariance preferences for the analysis of the firstprice, allpay auction. On the bidding side, we characterise the optimal strategy in symmetric allpay auctions under meanvariance preferences for general distributions of valuations and any number of bidders. We find that, in contrast to winnerpay auction formats, only hightype bidders increase their bids relative to the riskneutral case while low types minimise variance exposure by bidding low. Introducing asymmetric variance aversions across bidders into a Uniform valuations, twoplayer framework, we show that a more varianceaverse type bids always higher than her less varianceaverse counterpart. Taking meanvariance bidding behaviour as given, we show that an expected revenue maximising seller may want to optimally limit the number of participants. Although expected revenue for riskneutral bidders typically dominates revenue under meanvariance bidding, if the seller himself takes account of the variance of revenue, he may find it preferable to attract bidders endowed with meanvariance preferences. 
Keywords:  Auctions, contests, meanvariance preferences 
JEL:  C7 D7 D81 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:097&r=gth 