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on Game Theory |
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Issue of 2011‒01‒30
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Adam Kalai; Ehud Kalai |
| Abstract: | Selfish, strategic players may benefit from cooperation, provided they reach agreement. It is therefore important to construct mechanisms that facilitate such cooperation, especially in the case of asymmetric private information. The two major issues are: (1) singling out a fair and efficient outcome among the many individually rational possibilities in a strategic game, and (2) establishing a play protocol under which strategic players may achieve this outcome. The paper presents a general solution for two-person Bayesian games with monetary payoffs, under a strong revealed-payoff assumption. The proposed solution builds upon earlier concepts in game theory. It coincides with the von Neumann minmax value on the class of zero sum games and with the major solution concepts to the Nash Bargaining Problem. Moreover, the solution is based on a simple decomposition of every game into cooperative and competitive components, which is easy to compute. JEL Classification Numbers: C70, C71, C72, C78 |
| Date: | 2010–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1512&r=gth |
| By: | Mehmet Ekmekci; Andrea Wilson |
| Abstract: | We study the impact of unobservable replacements on the sustainability of reputation effects in frequently repeated games played by a long run player facing a sequence of short run players. At the beginning of every period the long-run player is replaced with a new long run player with a small probability. The new long run player is either a commitment type who plays the same strategy in every period when he is in the game, or a normal type. The long run player’s choice of stage game strategy is imperfectly observed by the short run players. We show that the long run player’s payoff, in any Nash equilibrium, is bounded below by what he could get by committing to his most favorite commitment type strategy after every history of the game, even as his rate of impatience vanishes at the same rate as his replacement probability. Hence arbitrarily infrequent replacements are sufficient to prevent reputations and their effects from disappearing when the stage game is played frequently enough. |
| Keywords: | Reputation, repeated games, replacements, disappearing reputations JEL Classification Numbers: D80, C73 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1511&r=gth |
| By: | Mehmet Ekmekci |
| Abstract: | In a product choice game played between a long lived seller and an infnite sequence of buyers, we assume that buyers cannot observe past signals. To facilitate the analysis of applications such as online auctions (e.g. eBay), online shopping search engines (e.g. BizRate.com) and consumer reports, we assume that a central mechanism observes all past signals, and makes public announcements every period. The set of announcements and the mapping from observed signals to the set of announcements is called a rating system. We show that, absent reputation effects, information censoring cannot improve attainable payoffs. However, if there is an initial probability that the seller is a commitment type that plays a particular strategy every period, then there exists a finite rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the seller is almost his Stackelberg payoff after every history. This is in contrast to Cripps, Mailath and Samuelson (2004), where it is shown that reputation effects do not last forever in such games if buyers can observe all past signals. We also construct .nite rating systems that increase payoffs of almost all buyers, while decreasing the seller’s payoff. |
| Keywords: | Reputations, Rating Systems, Online Reputation Mechanisms, Disappearing Reputations, Permanent Reputations. JEL Classification Numbers: D82 |
| Date: | 2010–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1505&r=gth |
| By: | Ralph-C. Bayer; Ludovic Renou |
| Abstract: | This paper investigates the relation between cognitive abilities and behavior in strategic-form games with the help of a novel experiment. The design allows us first to measure the cognitive abilities of subjects without confound and then to evaluate their impact on behaviour in strategic-from games. We find that subjects with better cognitive abilities show more sophisticated behavior and make better use of information on cognitive abilities and preferences of opponents. Although we do not find evidence for Nash behavior, observed behaviour is remarkably sophisticated, as almost 80% of subjects behave near optimal and outperform Nash behavior with respect to expected pay-offs. |
| Keywords: | cognitive ability; behaviours; strategic-form games; experiments; preferences; sophistication |
| JEL: | C70 C91 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:11/16&r=gth |
| By: | Nicolas Jacquemet (Centre d'Economie de la Sorbonne - Paris School of Economics); Frédéric Koessler (Paris-Jourdan Sciences Economiques) |
| Abstract: | This paper studies experimentally the value of private information in strictly competitive interactions with asymmetric information. We implement in the laboratory three examples from the class of zero-sum repeated games with incomplete information on one side and perfect monitoring. The stage games share the same simple structure, but differ markedly on how information should be optimally used once they are repeated. Despite the complexity of the optimal strategies, the empirical value of information coincides with the theoretical prediction in most instances. In particular, it is never negative, it decreases with the number of repetitions, and it is nicely bounded below by the value of the infinitely repeated game and above by the value of the one-shot game. Subjects are unable to completely ignore their information when it is optimal to do so, but the use of information in the lab reacts qualitatively well to the type and length of the game being played. |
| Keywords: | Concavification, laboratory experiments, incomplete information, value of information, zero-sum repeated games. |
| JEL: | C72 D82 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11002&r=gth |
| By: | Paolo Balduzzi (Università Cattolica Milano); Clara Graziano (Università degli Studi di Udine); Annalisa Luporini (Università degli Studi di Firenze, Dipartimento di Scienze Economiche) |
| Abstract: | We analyze the voting behavior of a small committee that has to approve or reject a proposal whose return is uncertain. Members have heterogenous preferences: some members want to maximize the expected value while other members have a bias toward project approval and ignore their private information. We analyze different voting games when information is costless and communication is not possible, and we provide insights on the optimal composition of these committees. Our main result is that the presence of biased members can improve the voting outcome by simplifying the strategies of unbiased members. Thus, committees with heterogeneous members can function at least as well as homogeneous committees and in some cases they perform better. In particular, when value-maximizing members hold 51% of votes, the socially optimal equilibrium becomes unique. |
| Keywords: | Voting, Small committees. |
| JEL: | D71 D72 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:frz:wpaper:wp2011_01.rdf&r=gth |
| By: | Itay P. Fainmesser; David A. Goldberg |
| Abstract: | We present a model of repeated games in large buyer-seller networks in the presence of reputation networks via which buyers share information about past transactions. The model allows us to characterize cooperation networks - networks in which each seller cooperates (by providing high quality goods) with every buyer that is connected to her. To this end, we provide conditions under which: [1] the incentives of a seller s to cooperate depend only on her beliefs with respect to her local neighborhood - a subnetwork that includes seller s and is of a size that is independent of the size of the entire network; and [2] the incentives of a seller s to cooperate can be calculated as if the network was a random tree with seller s at its root. Our characterization sheds light on the welfare costs of relying only on repeated interactions for sustaining cooperation, and on how to mitigate such costs. |
| Keywords: | Networks, moral hazard, graph theory, repeated games |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2011-2&r=gth |
| By: | Alcalde, Jose; Romero-Medina, Antonio |
| Abstract: | This paper proposes the notion of E-stability to conciliate Pareto efficiency and fairness. We propose the use of a centralized procedure, the Exchanging Places Mechanism. It endows students a position according with the Gale and Shapley students optimal stable matching as tentative allocation and allows the student to trade their positions. We show that the final allocation is E-stable, i.e. efficient, fair and immune to any justifiable objection that students can formulate. |
| Keywords: | School allocation problem; Pareto efficient matching |
| JEL: | D71 C71 |
| Date: | 2011–01–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:28206&r=gth |
| By: | Igal Milchtaich |
| Date: | 2011–01–17 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:661465000000001185&r=gth |
| By: | Luis Miller (Centre for Experimental Social Sciences, Nuffield College, University of Oxford); Christoph Vanberg (Department of Economics, University of Cambridge) |
| Abstract: | We conduct an experiment to assess the effects of different decision rules on the costs of decision making in a multilateral bargaining situation. Specifically, we compare the amount of costly delay observed in an experimental bargaining game under majority and unanimity rule. Our main finding is that individual subjects are more likely to reject offers under unanimity rule. This increased rejection rate, as well as the requirement that all subjects agree, leads to more costly delay. This result provides empirical support for a classic argument in favor of less-than-unanimity decision rules put forth by Buchanan and Tullock (1962). |
| Keywords: | Collective decision-making, Majority rule, Unanimity, Legislative bargaining, Experimental economics |
| JEL: | C78 C92 D71 D72 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:cex:dpaper:2011002&r=gth |
| By: | Elyès Jouini (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX); Clotilde Napp (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris Dauphine - Paris IX); Yannick Viossat (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) |
| Abstract: | We provide a discipline for belief formation through a model of subjective beliefs, in which agents hold strategic beliefs. More precisely, we consider beliefs as a strategic variable that agents can choose (consciously or not) in order to maximize their utility at the equilibrium. These strategic beliefs result from an evolutionary process. We find that evolutionary strategic behavior leads to belief subjectivity and heterogeneity. Optimism (resp. overconfidence) as well as pessimism (resp. doubt) both emerge from the evolution process. Furthermore, we obtain a positive correlation between pessimism (rep. doubt) and risk-tolerance. We analyse the equilibrium characteristics. Under reasonable assumptions, the consensus belief is pessimistic and, as a consequence, the risk premium is higher than in a standard setting. |
| Keywords: | Beliefs formation, strategic beliefs, optimal beliefs, distorded beliefs, pessimism, risk premium |
| Date: | 2010–12–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00556490&r=gth |
| By: | Sergio Currarini (Department of Economics, University Of Venice Cà Foscari); Fernando Vega Redondo (European University Institute) |
| Abstract: | We study the formation of social ties among heteogeneous agents in a model where meetings are governed by agents' directed search. The aim is to shed light on the important issue of homophily (the tendency of agents to connect with others of the same type). The essential contribution of the model is to provide a basic microfoundation for the opportunity/meeting biases that, as the literature highlights, are a crucial element of the phenomenon. Under the assumption that search is more effective in large pools, the equilibrium is characterized by a threshold in terms of group size: large groups only search among similar agents while smaller groups search in the whole population. This threshold behavior is consistent with the empirical evidence observed in a range of social environments such as high school friendships and interethnic marriages. And assuming that search is subject to small frictions, it also generates the bell-shaped form of the so-called Coleman index observed in the data. Other implications of the model supported by the evidence concern the pattern of cross-group ties among small groups, the linearity of excess homophily for large groups, and the positive effect on it of overall population size. |
| Keywords: | Homophily, search, social networks, segregation. |
| JEL: | D7 D71 D85 Z13 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2010_24&r=gth |