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on Game Theory |
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Issue of 2013‒10‒11
nine papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Chirantan Ganguly; Indrajit Ray |
| Abstract: | We consider a Battle of the Sexes game with two types, High and Low, for each player and allow cheap talk regarding players' types before the game. We prove that the unique fully revealing symmetric cheap talk equilibrium exists for a low range of prior probability of the High-Type. This equilibrium has a desirable type-coordination property: it fully coordinates on the ex-post efficient pure Nash equilbrium when the players' types are different. Type-coordination is also obtained in a partially revealing equilibrium in which only the High-type is not truthful, for a medium range of prior probability of the High-type. |
| Keywords: | Battle of the Sexes, Private Information, Cheap Talk, Coordination, Full Revelation |
| JEL: | C72 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:13-01r&r=gth |
| By: | Frédéric Schneider; Roberto A. Weber |
| Abstract: | We study how the willingness to enter long-term bilateral relationships affects cooperation even when parties have little information about each other, ex ante, and cooperation is otherwise unenforceable. We experimentally investigate a finitely-repeated Prisoner’s Dilemma, allowing players to endogenously select interaction durations. Consistent with prior research, longer interactions facilitate cooperation. However, many individuals avoid long-term commitment, with uncooperative types less likely to commit than conditional cooperators. Endogenously chosen long-term commitment yields higher cooperation rates (98% in one condition) than exogenously imposed commitment. Thus, the willingness to enter into long-term relationships provides a means for fostering - and screening for - efficient cooperation. |
| Keywords: | Repeated games, cooperation, voluntary commitment |
| JEL: | C72 C92 D03 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:130&r=gth |
| By: | Laurent Lehmann; Georg Nöldeke; Jorge Peña (University of Basel) |
| Abstract: | In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability properties of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as it is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis. |
| Keywords: | evolutionary game theory, multi-player matrix games, replicator dynamics, public goods games, gains from switching, polynomials in Bernstein form 2 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:bsl:wpaper:2013/13&r=gth |
| By: | Sergiu Hart; Noam Nisan |
| Abstract: | We consider the complexity of finding a Correlated Equilibrium in an n-player game in a model that allows the algorithm to make queries for players' utilities at pure strategy profiles. Many randomized regret-matching dynamics are known to yield an approximate correlated equilibrium quickly: in time that is polynomial in the number of players, n, the number of strategies of each player, m, and the approximation error, 1/?. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate equilibrium and no efficient randomized algorithm can reach an exact equilibrium. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp647&r=gth |
| By: | Einy, E; Haimanko, O; Moreno, D; Sela, A; Shitovitz, B |
| Abstract: | Under standard assumptions about players’ cost functions, we show that a Tullock contest with asymmetric information has a pure strategy equilibrium. Moreover, when players have a common value and a common state independent linear cost function, a two player Tullock contest in which one player has an information advantage has a unique equilibrium. In this equilibrium both players exert the same expected effort, although the player with information advantage has a greater payoff and wins the prize less frequently than his opponent. When there are more than two players in the contest, an information advantage leads to higher payoffs, but the other properties of equilibrium no longer hold. |
| JEL: | C72 D44 D82 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2013-11&r=gth |
| By: | Sergiu Hart; Andreu Mas-Colell |
| Abstract: | Inspired by the existing work on correlated equilibria and regret-based dynamics in games, we carry out a first exploration of the links between the leading equilibrium concept for (exchange) economies, Walrasian equilibrium, and the dynamics, specifically regret-matching dynamics, of trading games that fit the economic structure and have the property that their pure Nash equilibria implement the Walrasian outcomes. Interestingly, in the case of quasilinear utilities (or "transferable utility"), all the concepts essentially coincide, and we get simple deterministic dynamics converging to Walrasian outcomes. Connections to sunspot equilibria are also studied. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp648&r=gth |
| By: | Larry G. Epstein (Department of Economics, Boston University); Kyoungwon Seo |
| Abstract: | We generalize de Finetti’s exchangeable Bayesian model to accommodate ambiguity. As a central motivating example, we consider a policy maker facing a cross-section of markets in which …rms play an entry game. Her theory is Nash equilibrium and it is incomplete because there are multiple equilibria and she does not understand how equilibria are selected. This leads to partial identi…cation of parameters when drawing inferences from realized outcomes in some markets and to ambiguity when considering (policy) decisions for other markets. We model both her inference and choice. |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2013-001&r=gth |
| By: | Timo Hiller; Timo Hiller |
| Abstract: | This paper presents a simple model of strategic network formation with local complementarities in effort levels and positive local externalities for a general class of payoff functions. Results are obtained for one-sided and two-sided link creation. In both cases (pairwise) Nash equilibrium networks are nested split graphs, which are a strict subset of core-periphery networks. The relevance of the convexity of the value function (gross payoffs as a function of neighbours' effort levels when best responding) in obtaining nested split graphs is highlighted. Under additional assumptions on payoffs, we show that the only efficient networks are the complete and the empty network. Furthermore, there exists a range of linking cost such that any (pairwise) Nash equilibrium is inefficient and for a strict subset of this range any (pairwise) Nash equilibrium network structure is different from the efficient network. These findings are relevant for a wide range of social and economic phenomena, such as educational attainment, criminal activity, labor market participation, and R&D expenditures of rms. |
| Keywords: | Strategic network formation, peer effects, strategic complements, positive externalities. |
| JEL: | D62 D85 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stitep:/2013/564&r=gth |
| By: | Gavrilova, Evelina |
| Abstract: | In this paper I analyze partnership formation within the property crime market in the United States. I develop a static matching model, in which a criminal forms a partnership with a counterpart with the same probability of success. Using individual arrest data from the National Incident Based Reporting System, I pinpoint matches where the underlying ability of two partners differ. This difference in ability is correlated to observable characteristics, making the case for discrimination. By comparing the regression results to success means for the same demographic groups, I find patterns consistent with discrimination. Beside the patterns of gender and racial segregation, I find that in white-black matches, blacks outperform whites, consistent with success means. In male-female matches the female's success realization is higher than the male's, contrary to the difference in success means, where males on average outperform females, hinting at a distaste premium. |
| Keywords: | Assortative Matching, Bias, Crime, Discrimination, Organized Crime |
| JEL: | C78 J16 J71 K42 |
| Date: | 2013–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:50432&r=gth |