
on Game Theory 
Issue of 2013‒07‒28
seven papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Jianpei Li; Paul Schweinzer 
Abstract:  We study the incentives of noncooperative players to play a cooperative game. That is, we look for individually rational, redistributive, pregame agreements enacted in order to coordinate towards efficient equilibrium play. Contrasting with standard Nash equilibrium analysis, we assume that players can commit to the agreements they negotiate and that utility is verify and transferable. We show that agreeing on a proportionalexponential redistribution rule is individually rational and implements the socially efficient outcome as Nash equilibrium. Moreover, we show that this class of redistributional contracts may be naturally obtained as the outcome of Nash bargaining. 
Keywords:  Redistribution, Efficiency, Social contract 
JEL:  C72 D62 D71 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:yor:yorken:13/19&r=gth 
By:  Dominik Karos (Department of Economics and Statistics, Saarland University) 
Abstract:  Given a simple game, a power configuration specifies the power of each player in each winning coalition. We introduce a new power configuration which takes into account bargaining among players in coalitions. We show that under very weak conditions on a bargaining solution there is a power configuration which is stable with respect to renegotiations. We further show that given this power configuration there is a coalition which is both internally and Nash stable. We consider two different bargaining solutions on apex games and show under which conditions there are core stable coalitions. Finally, we investigate how infeasible coalition might affect the outcome and apply our model to the German parliament. 
Keywords:  Coalition Formation, Power, Bargaining 
JEL:  C71 D71 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2013.63&r=gth 
By:  Philippe Bich (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Rida Laraki (Ecole Polytechnique  Ecole Polytechnique, IMJ  Institut de Mathématiques de Jussieu  CNRS : UMR7586  Université Pierre et Marie Curie (UPMC)  Paris VI  Université Paris VII  Paris Diderot) 
Abstract:  New relaxations of the Nash equilibrium concept are shown to exist in any strategic game with discontinuous payoff functions. The new concepts are used (1) to show the equivalence between Reny's betterreply security condition [28] and SimonZame's endogenous tiebreaking rule equilibrium concept [32], (2) to obtain conditions for the existence of approximated equilibria in a class of discontinuous games that naturally extends Reny's betterreply secure games, and (3) to show the existence of approximated equilibria in a large family of twoplayer games that contains all standard models of auctions. 
Keywords:  Discontinuous games, betterreply security, sharingrule equilibrium, approximated equilibrium, strategic approximation, auctions, diagonal games. 
Date:  2013–07–18 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:hal00846143&r=gth 
By:  Ezra Einy (Department of Economics, BenGurion University of the Negev, Israel); Ori Haimanko (Department of Economics, BenGurion University of the Negev, Israel); Diego Moreno (Departamento de Economia, Universidad Carlos III de Madrid.); Aner Sela (Department of Economics, BenGurion University of the Negev. Israel); Benyamin Shitovitz (Department of Economics, University of Haifa) 
Abstract:  Under standard assumptions about players'cost functions, we show that a Tullock contest with asymmetric information has a pure strategy equilibrium. Next we study Tullock contests in which players have a common value and a common stateindependent linear cost function. A twoplayer contest in which one player has an information advantage has a unique equilibrium. In equilib rium both players exert the same expected effort, and although the player with an information advantage wins the prize with probability less than onehalf, his payoff is greater or equal to that of his opponent. When there are more than two players in the contest, having information advantage leads to higher payoffs, but the other properties of equilibrium no longer hold. 
JEL:  C72 D44 D82 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:bgu:wpaper:1303&r=gth 
By:  Norde, H.W. (Tilburg University, Center for Economic Research) 
Abstract:  Abstract: In this paper two cost sharing solutions for minimum cost spanning tree problems are introduced, the degree adjusted folk solution and the cost adjusted folk solution. These solutions overcome the problem of the classical reductionist folk solution as they have considerable strict ranking power, without breaking established axioms. As such they provide affirmative answers to open questions, put forward in Bogomolnaia and Moulin (2010) and Bogomolnaia et al. (2010). 
Keywords:  cost sharing;minimum cost spanning tree games;networks. 
JEL:  C71 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:2013039&r=gth 
By:  Lee, Byung Soo 
Abstract:  In this paper, we establish the Bayesian foundations of type structures in which beliefs are lexicographic probability systems (LPS’s)—such as those used in Brandenburger et al. (2008)—rather than standard probability measures as in Mertens and Zamir (1985). This is a setting which the distinction between preferences hierarchies (Epstein and Wang, 1996) and beliefs hierarchies is meaningful and the former has conceptual advantages. Type structures in which beliefs are conditional probability systems (CPS’s) are found to describe fewer hierarchies than LPS type structures can if a nonredundancy requirement is imposed. The two families of type structures are found to be capable of describing the same set of hierarchies in the absence of such a requirement. The existence of “largest”—a notion closely related to universality—LPS/CPS type structures is also shown. Finally, we find that some coherent hierarchies cannot be types but those hierarchies may be needed to express epistemic conditions for iterated elimination of weakly dominated strategies. 
Keywords:  Preferences hierarchies, type structure, weakly dominated strategies, epistemic game theory, lexicographic probability system, conditional probability system 
JEL:  C72 D8 D80 
Date:  2013–07–17 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48551&r=gth 
By:  Lombardi, Michele; Yoshihara, Naoki 
Abstract:  Given the framework introduced by Dutta and Sen (2012), this paper offers a comprehensive analysis of (Nash) implementation with artially honest agents when there are three or more participants. First, it establishes a condition which is necessary and sufficient for implementation. Second, it provides simple tests for checking whether or not a social choice correspondence can be implemented. Their usefulness is shown by examining implementation in a wide variety of environments. 
Keywords:  Implementation, Nash equilibrium, social choice correspondences, partial honesty, Condition μ 
JEL:  C72 D71 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:hit:ccesdp:49&r=gth 