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on Game Theory |
| By: | Parkash Chander (Jindal School of Government and Public Policy); Myrna Wooders (Vanderbilt University) |
| Abstract: | We propose a cooperative solution concept for games in extensive form that incorporates both cooperation and subgame perfection. This new concept, which we label the subgame-perfect core, is a refinement of the core of an extensive game in the same sense as the set of subgame-perfect Nash equilibria is a refinement of the set of Nash equilibria. Moreover, each subgame perfect core payoff vector can be obtained as a subgame-perfect Nash equilibrium payoff vector of a modified extensive game. We establish several additional properties of the subgame-perfect core and demonstrate its applicability by studying three applications: the centipede game, the two-player infinite bargaining game of alternating offers, and a dynamic game of climate change. In addition, we motivate and introduce a concept of subgame-perfect strong Nash equilibrium of an extensive game and show that it is coalition proof. |
| Keywords: | Extensive game, subgame perfection, characteristic function game, core, centipede game, coalition-proof Nash equilibrium |
| JEL: | C7 D0 |
| Date: | 2016–03–13 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-sub-16-00009&r=gth |
| By: | Benjamin Sperisen (Department of Economics, Tulane University) |
| Abstract: | Reputation models typically assume players have full memory, yet in many applications this does not hold. This paper studies incomplete information games where players observe only finitely many recent periods, deriving a recursive characterization of the equilibrium payoff set that captures both stationary and previously unexplored non-stationary equilibria, as well as tools for studying purifiable (i.e. robust to payoff perturbations) equilibria. These tools are applied to a product choice game. For 1-period memory, I obtain the exact minimum and maximum purifiable equilibrium payoffs for almost all discount factors and prior beliefs on an "honest" firm type. For long memory, I characterize the minimum purifiable non-stationary equilibrium payoff and unique stationary payoff. In both cases, incomplete information and non-stationary behavior qualitatively change the equilibrium payoff set. These results hold for fixed discount factors independent of prior beliefs, and so do not require extreme patience. |
| Keywords: | Reputation, bounded memory, purifiability, product choice game |
| JEL: | C73 D82 D83 L14 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:tul:wpaper:1602&r=gth |
| By: | Marie Laclau (CNRS - Centre National de la Recherche Scientifique, PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - EHESS - École des hautes études en sciences sociales - Institut national de la recherche agronomique (INRA) - École des Ponts ParisTech (ENPC) - CNRS - Centre National de la Recherche Scientifique, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Tristan Tomala (HEC Paris - Department of Economics and Decision Sciences) |
| Abstract: | We consider repeated games with compact actions sets and pure strategies in which players commonly observe a public signal which reveals imperfectly the action profile. We characterize the set of payoffs profiles that can be sustained by a perfect equilibrium, as players become increasingly patient. There are two conditions: admissibility and joint rationality. An admissibly feasible payoff can be achieved by an action profile that offers no unilateral deviation which is both undetectable and profitable. It is jointly rational if for all weights on players, the weighted payoff is greater than or equal to the minmax level of the weighted payoff function. This characterization is alternative to the one provided by the " score method " of Fuden-berg and Levine (1994). We provide a simple construction of equilibrium strategies based on cooperation, punishments and rewards. Punishments rely on Blackwell's approachability algorithm. |
| Keywords: | Repeated games, approachability, imperfect public monitoring. |
| Date: | 2016–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:hal-01285326&r=gth |
| By: | Danz, David Nils; Huck, Steffen; Jehiel, Philippe |
| Abstract: | We study how subjects in an experiment use different forms of public information about their opponents' past behavior. In the absence of public information, subjects appear to use rather detailed statistics summarizing their private experiences. If they have additional public information, they make use of this information even if it is less precise than their own private statistics - except for very high stakes. Making public information more precise has two consequences: It is also used when the stakes are very high and it reduces the number of subjects who ignore any information - public and private. That is, precise public information crowds in the use of own information. Finally, our results shed some light on unravelling in centipede games. |
| Keywords: | backward induction,analogy-based expectation equilibrium,learning,experiment |
| JEL: | C72 C92 D83 D84 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2016201&r=gth |
| By: | Bolle, Friedel; Spiller, Jörg |
| Abstract: | In Binary Threshold Public Good (BTPG) games players contribute or not to the production of a public good which is produced if and only if there are "enough" contributors. There is a plethora of equilibria in BTPG games. We experimentally test general theoretical attributes of equilibria and proposals for equilibrium selection. As theory predicts, if the cost/benefit ratio is the same, then subjects play (almost) the same mixture of strategies and, after switching from a positive to a negative frame, the theoretically expected "mirrored" behavior can be observed, i.e. contrary to most linear Public Good experiments we do not find a framing effect. A finite mixture model successfully (i.e. without rejection in a chi-square test) describes behavior in all eight experimental games (same parameters for four thresholds and positive/negative frame). The Harsanyi-Selten theory of equilibrium selection is moderately supported. Efficiency as an equilibrium selection device and also risk dominance are clearly rejected. |
| Keywords: | Binary Threshold Public Goods,framing,equilibrium selection,payoff dominance,risk dominance,efficiency,experiment |
| JEL: | C72 D72 H41 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:euvwdp:379&r=gth |
| By: | Alexandre Skoda (Centre d'Economie de la Sorbonne) |
| Abstract: | We consider restricted games on weighted communication graphs associated with minimum partitions. We replace in the classical definition of Myerson's graph-restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with Pmin. Then we establish that these conditions are also sufficient for a weaker condition, called F-convexity, obtained by restriction of convexity to connected subsets. Moreover we show that Myerson's game associated to a given graph G can be obtained as a particular case of the Pmin-restricted game for a specific weighted graph G'. Then we prove that G is cycle-complet if and only if a specific condition on adjacent cycles is satisfied on G' |
| Keywords: | Communication networks; cooperative game; restricted game; partitions |
| JEL: | C7 C71 C6 C61 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16019&r=gth |
| By: | De Francesco, Massimo A.; Salvadori, Neri |
| Abstract: | The paper is the second part of a trilogy in which we extend the analysis of price competition among capacity-constrained sellers beyond duopoly to triopoly. In the first part of the trilogy we provided some general results, highlighting features of a duopolistic mixed strategy equilibrium that generalize to triopoly and provided a first partition concerning the pure strategy equilibrium regions and the mixed strategies equilibrium region and then the partition of this region in a part in which the payoffs of the two smallest firm are proportional to their capacities and another in which the smallest firm obtains a payoff proportinally higher than that of the middle sized firm. In this paper we provide a complete characterization of the set of mixed strategy equilibria in the part in which the payoffs of the two smallest firms are proportional to their capacities. This part is partitioned according to equilibrium features and in each part it is determined whether equilibria are uniquely determined or not and in the latter case it is proved that the equilibria constitute a continuum. Further we determine the circustances in which supports of an equilibrium strategy may be disconnected and show how gaps are then determined. We also prove that the union of supports is indeed connected, a property which cannot be extended to the case in which the smallest firm obtains a payoff proportinally higher than that of the middle sized firm. The third part of the trilogy will be devoted to a complete characterization of the mixed strategy equilibria when the smallest firm obtains a payoff proportinally higher than that of the middle sized firm. This will allow also to determine the payoff of the smallest firm. |
| Keywords: | Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium |
| JEL: | C72 D43 L13 |
| Date: | 2016–03–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69999&r=gth |
| By: | James Andreoni; Michael A. Kuhn; Larry Samuelson |
| Abstract: | We report experimental results for a twice-played prisoners’ dilemma in which the players can choose the allocation of the stakes across the two periods. Our point of departure is the assumption that some (but not all) people are principled to “do the right thing,” or cooperate, as long as their opponent is sufficiently likely to do so. The presence of such types can be exploited to enhance cooperation by structuring the twice-played prisoners’ dilemma to “start small,” so that the second-stage stakes are larger (but not too much larger) than the first-stage stakes. We compare conditions where the allocation of stakes is chosen exogenously to conditions where it is chosen by the players themselves. We show that players are able to find and choose the payoff maximizing strategy of starting small in a twice-played prisoners’ dilemma, and that the salutary payoff effects of doing so are larger than those that arise when the same allocation is exogenously chosen. |
| JEL: | C92 D64 Z13 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21934&r=gth |
| By: | Jackson, Matthew O. (Stanford University); Rogers, Brian (Washington University); Zenou, Yves (Monash University,, Department of Economics,) |
| Abstract: | We survey the literature on the economic consequences of the structure of social networks. We develop a taxonomy of `macro' and `micro' characteristics of social interaction networks and discuss both the theoretical and empirical findings concerning the role of those characteristics in determining learning, diffusion, decisions, and resulting behaviors. We also discuss the challenges of accounting for the endogeneity of networks in assessing the relationship between the patterns of interactions and behaviors. |
| Keywords: | Social networks; Social economics; Homophily; Diffusion; Social learning contagion; Centrality measures; Endogeneity; Network formation |
| JEL: | C72 D85 L14 Z13 |
| Date: | 2016–03–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:iuiwop:1116&r=gth |
| By: | Woods, Daniel; Servátka, Maroš |
| Abstract: | This paper studies psychological forward induction and the updating of beliefs in the lost wallet game (Dufwenberg & Gneezy, 2000), which is required to derive a prediction for guilt averse agents. Our experiment tests whether the second movers psychologically induct forward and update their beliefs after observing their paired first movers’ decision by eliciting beliefs with different second mover knowledge of first mover decision, depending on treatment. We find that second movers do update their beliefs conditional on receiving information on the first mover’s action, supporting psychological forward induction. |
| Keywords: | beliefs, experiment, guilt aversion, lost wallet game, psychological forward induction, updating |
| JEL: | C70 C91 |
| Date: | 2016–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69957&r=gth |
| By: | Heinz, Matthias; Schumacher, Heiner |
| Abstract: | We examine what an applicant´s vita signals to potential employers about her willingness to cooperate in teams. Intensive social engagement may credibly reveal that an applicant cares about the well-being of others and therefore is less likely to free-ride in teamwork situations. We find that contributions in a public goods game strongly increase in a subject´s degree of social engagement as indicated on her résumé (and rated by an independent third party). Engagement in other domains, such as student or sports associations, is not positively correlated with contributions. In a prediction experiment with human resource managers from various industries, we find that managers use résumé content effectively to predict relative differences in subjects´ willingness to cooperate. Thus, young professionals signal important behavioral characteristics to potential employers through the choice of their extracurricular activities. |
| Keywords: | signaling,public goods,labor markets,extracurricular activities |
| JEL: | C72 C92 D82 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:safewp:120&r=gth |
| By: | Tena, Juan de Dios; Wiper, Michael P.; Corona, Francisco |
| Abstract: | Identifying the important matches in international football tournaments is of great relevance for a variety of decision makers such as organizers, team coaches and/or media managers. This paper addresses this issue by analyzing the role of the statistical approach used to estimate the outcome of the game on the identification of decisive matches on international tournaments for national football teams. We extend the measure of decisiveness proposed by Geenens (2014) in order to allow us to predict or evaluate match importance before, during and after of a particular game on the tournament. Using information from the 2014 FIFA World Cup, our results suggest that Poisson and Kernel regressions significantly outperform the forecasts of ordered probit models. Moreover, we find that the identification of the key, but not most important, matches depends on the model considered. We also apply this methodology to identify the favorite teams and to predict the most important matches in 2015 Copa America before the start of the competition. |
| Keywords: | Kernel regression; Poisson model; Entropy; Ordered probit model; Game importance |
| Date: | 2015–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:21174&r=gth |
| By: | Hiromasa Takahashi (Faculty of International Studies, Hiroshima City University); Junyi Shen (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan); Kazuhito Ogawa (Faculty of Sociology and Center for Experimental Economics, Kansai University) |
| Abstract: | We examine gender-specific reference-dependent preferences in a trust game experiment. Different participation fees and one question eliciting subjects' reference points were used to categorize subjects into three frames: the gain frame, gain or loss frame, and loss frame. We find that (i) men are risk-seeking in both the gain and the loss frame; (ii) women are not always more risk-averse than men; and (iii) women display other-regarding preferences only when they are in the gain frame. These results demonstrate the importance of taking account of both gender differences and reference-dependent preferences when examining individuals' economic behavior. |
| Keywords: | Reference-dependent preference, Gender difference, Trust game experiment, Risk preference, Other-regarding preference |
| JEL: | C72 C91 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2016-09&r=gth |
| By: | Choy, James P. (University of Warwick) |
| Abstract: | Many societies are divided into multiple smaller groups. Certain kinds of interaction are more likely to take place within a group than across groups. I model a reputation effect that enforces these divisions. Agents who interact with members of different groups can support lower levels of cooperation with members of their own groups. A hierarchical relationship between groups appears endogenously in equilibrium. Group divisions appear without any external cause, and improvements in formal contracting institutions may cause group divisions to disappear. Qualitative evidence from the anthropological literature is consistent with several predictions of the model. |
| Keywords: | Cooperation, Caste, Social Institution JEL Classification: C73, O12, O17 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:cge:wacage:266&r=gth |
| By: | Lombardi, Michele; Yoshihara, Naoki |
| Abstract: | An individual may display an honesty standard which allows her to lie a little without that being harmful to her self view as an honest person. On this basis, the paper considers a society with a finite number of individuals involving partially-honest individuals and in which every individual has her own honesty standard. An individual honesty standard is modeled as a subgroup of the society, including the individual herself. A partially-honest individual is an individual who strictly prefers to tell the truth prescribed by her honesty standard whenever lying has no effect on her material well-being. The paper studies the impact of placing honesty standard restrictions on the mechanism designer for Nash implementation problems of that society. It offers a necessary condition for Nash implementation, called partial-honesty monotonicity, and shows that in an independent domain of preferences that condition is equivalent to Maskin monotonicity, provided that honesty standards of society are non-connected. They are non-connected if every individual is excluded from the honesty standard of another individual. Finally, it shows that the limitations imposed by Maskin monotonicity can be circumvented by a q-mechanism (Lombardi and Yoshihara, 2013) provided that there are at least n - q + 1 partially-honest individuals in a society and that no participant has a veto-power. |
| Keywords: | Nash implementation, partial-honesty, non-connected honesty standards, independent domain, q-mechanisms |
| JEL: | C72 D71 D82 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:633&r=gth |
| By: | HORAN, Sean |
| Abstract: | I provide choice-theoretic foundations for a simple two-stage model, called transitive shortlist methods, where choices are made by sequentially by applying a pair of transitive preferences (or rationales) to eliminate inferior alternatives. Despite its simplicity, the model accommodates a wide range of choice phenomena including the status quo bias, framing, homophily, compromise, and limited willpower. I establish that the model can be succinctly characterized in terms of some well-documented context effects in choice. I also show that the underlying rationales are straightforward to determine from readily observable reversals in choice. Finally, I highlight the usefulness of these results in a variety of applications. |
| Keywords: | Shortlisting; axiomatization; revealed preference; identification |
| JEL: | D01 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montde:2016-01&r=gth |
| By: | Drew Fudenberg; David K Levine |
| Date: | 2016–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:786969000000001307&r=gth |
| By: | Hervés-Estévez, Javier; Moreno-García, Emma |
| Abstract: | We introduce a new notion of bargaining set for finite economies and show a convergence result. |
| Keywords: | Bargaining set, coalitions, core, veto mechanism, justified objections. |
| JEL: | D00 D11 D51 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69813&r=gth |
| By: | Eric W Bond (Vanderbilt University); Kamal Saggi (Vanderbilt University) |
| Abstract: | We analyze bargaining between a developing country (South) and a multinational firm over the local price of its patented product. We use an alternating offers bargaining game in which the South can resort to compulsory licensing (CL) if the two parties fail to reach agreement by a certain deadline. The presence of international price spillovers introduces two novel features into the standard bargaining problem: (i) the surplus from entry prior to the CL deadline may be negative and (ii) CL can yield higher surplus than entry. We establish conditions under which equilibrium may exhibit immediate entry, preemptive entry just prior to the CL deadline, or the occurrence of CL. The South necessarily gains from the threat of CL if the joint payoff under entry is higher relative to CL but can lose if it is lower. |
| Keywords: | Patented Goods, Compulsory Licensing, Bargaining, Quality, Welfare. |
| JEL: | F1 C7 |
| Date: | 2016–03–13 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-sub-16-00008&r=gth |