
on Game Theory 
By:  Francis Bloch; Geoffroy de Clippel 
Abstract:  This paper studies the core of combined games, obtained by summing two coalitional games. It is shown that the set of balanced transferable utility games can be partitioned into equivalence classes of component games to determine whether the core of the combined game coincides with the sum of the cores of its components. On the other hand, for nonbalanced games, the binary relation associating two component games whose combination has an empty core is not transitive. However, we identify a class of nonbalanced games which, combined with any other nonbalanced game, has an empty core. 
Keywords:  Cooperative Game; Core; Additivity; Issue Linkage; Multi Issue Bargaining 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:bro:econwp:20091&r=gth 
By:  Daniel John Zizzo (University of East Anglia, School of Economics, Norwich, UK); Jonathan H.W. Tan (Nottingham University Business School, UK) 
Abstract:  Game harmony describes how harmonious (nonconflictual) or disharmonious (conflictual) the interests of players are in a game, as embodied in the game? raw payoffs. It departs from the traditional gametheoretic approach in that it is a non equilibrium behavioral approach which can be psychologically founded. We experimentally test the predictive power of basic game harmony measures on a variety of wellknown 2×2 games and randomlygenerated 2×2 and 3×3 generic games. Our findings support its all rounded predictive power. Game harmony provides an alternative tool that is both powerful and parsimonious, as it does not require information on a subject? degree of rationality, social preferences, beliefs and perceptions are required. 
Keywords:  games, game harmony, cooperation, behavioral economics. 
Date:  2009–07–13 
URL:  http://d.repec.org/n?u=RePEc:bbr:workpa:4&r=gth 
By:  Olivier Gossner; Ehud Kalai; Robert Weber 
Abstract:  In Bayesian environments with private information, as described by the types of Harsanyi, how can types of agents be (statistically) disassociated from each other and how are such disassociations reflected in the agents’ knowledge structure? Conditions studied are (i) subjective independence (the opponents’ types are independent conditional on one’s own) and (ii) type disassociation under common knowledge (the agents’ types are independent, conditional on some commonknowledge variable). Subjective independence is motivated by its implications in Bayesian games and in studies of equilibrium concepts. We find that a variable that disassociates types is more informative than any commonknowledge variable. With three or more agents, conditions (i) and (ii) are equivalent. They also imply that any variable which is common knowledge to two agents is common knowledge to all, and imply the existence of a unique commonknowledge variable that disassociates types, which is the one defined by Aumann. 
Keywords:  Bayesian games, independent types, common knowledge. 
JEL:  D80 D82 C70 
Date:  2009–07 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1476&r=gth 
By:  Leonidas, Spiliopoulos 
Abstract:  This paper addresses the question of whether neural networks (NNs), a realistic cognitive model of human information processing, can learn to backward induce in a twostage game with a unique subgameperfect Nash equilibrium. The NNs were found to predict the Nash equilibrium approximately 70% of the time in new games. Similarly to humans, the neural network agents are also found to suffer from subgame and truncation inconsistency, supporting the contention that they are appropriate models of general learning in humans. The agents were found to behave in a bounded rational manner as a result of the endogenous emergence of decision heuristics. In particular a very simple heuristic socialmax, that chooses the cell with the highest social payoff explains their behavior approximately 60% of the time, whereas the ownmax heuristic that simply chooses the cell with the maximum payoff for that agent fares worse explaining behavior roughly 38%, albeit still significantly better than chance. These two heuristics were found to be ecologically valid for the backward induction problem as they predicted the Nash equilibrium in 67% and 50% of the games respectively. Compared to various standard classification algorithms, the NNs were found to be only slightly more accurate than standard discriminant analyses. However, the latter do not model the dynamic learning process and have an ad hoc postulated functional form. In contrast, a NN agent’s behavior evolves with experience and is capable of taking on any functional form according to the universal approximation theorem. 
Keywords:  Agent based computational economics; Backward induction; Learning models; Behavioral game theory; Simulations; Complex adaptive systems; Artificial intelligence; Neural networks 
JEL:  C45 C7 C73 
Date:  2009–09–12 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:17267&r=gth 
By:  Ciuiu, Daniel 
Abstract:  In this paper we will solve some linear programming problems by solving systems of differential equations using game theory. The linear programming problem must be a classical constraints problem or a classical menu problem, i.e. a maximization/minimization problem in the canonical form with all the coefficients (from objective function, constraints matrix and right sides) positive. Firstly we will transform the linear programming problem such that the new problem and its dual have to be solved in order to find the Nash equilibrium of a matriceal game. Next we find the Nash equilibrium by solving a system of differential equations as we know from evolutionary game theory, and we express the solution of the obtained linear programming problem (by the above transformation of the initial problem) using the Nash equilibrium and the corresponding mixed optimal strategies. Finally, we transform the solution of the obtained problem to obtain the solution of the initial problem. We make also a program to implement the algorithm presented in the paper. 
Keywords:  Linear programming; evolutionary game theory; Nash equilibrium. 
JEL:  C61 C73 C72 
Date:  2009–06 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:17191&r=gth 
By:  Ingela Alger (Department of Economics, Carleton University) 
Abstract:  How can a desire to cooperate in oneshot interactions survive, even though it gives a material disadvantage to its carrier? I analyze this issue using a oneshot public goods game between two altruistic individuals. Within a pair, the least altruistic individual is better off materially. Between pairs, individuals in the pair with the highest degree of altruism are better off materially. I determine the evolutionarily stable degree of altruism, allowing for assortative matching. The stable degree of altruism is strictly smaller than the degree of assortativity, and it may be negative. It is also increasing in the degree of assortativity. For a given degree of assortativity, the stable degree of altruism depends on the relative strength of the withinpair and the betweengroup e¤ect on material welfare. This relative strength in turn depends on the production and cost functions in the underlying public goods game. 
Keywords:  public goods, teamwork, altruism, evolution of preferences, evolutionary stability 
JEL:  D02 D13 
Date:  2009–08–26 
URL:  http://d.repec.org/n?u=RePEc:car:carecp:0906&r=gth 
By:  Sergio Currarini (Department of Economics,Faculty of Economics, Università degli Studi di Venezia "Ca' Foscari"); Marco Marini (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy)) 
Abstract:  This paper revisits a particular behaviour for rms competing in imperfect competitive markets, underlying the well known model of kinked demand curve. We show that under some symmetry and regularity conditions, this asymmetric behaviour of rms sustains monopoly pricing, and possesses therefore some "rationality" interpretation. We also show that such a behaviour can be generalized and interpreted as a norm of behaviour that sustains efficient outcomes in a more general class of symmetric games. 
Keywords:  Kinked Demand, Symmetric Games, Norms of Behaviour. 
JEL:  C70 D21 D43 L13 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:urb:wpaper:09_05&r=gth 
By:  Geoffroy de Clippel 
Abstract:  Most contributions in axiomatic bargaining are phrased in the space of utilities. This comes in sharp contrast with standards in most other fields of economic theory. The present paper shows how Nash’s original axiomatic system can be rephrased in a natural class of economic environments with lotteries, and how his uniqueness result can be recovered, provided one completes the system with a property of independence with respect to preferences over unfeasible alternatives. Similar results can be derived for the KalaiSmorodinsky solution if and only if bargaining may involve multiple goods. The paper also introduces a distinction between welfarism and cardinal welfarism, and emphasizes that the Nash solution is ordinally invariant on the class of von NeumannMorgensterm preferences. 
Keywords:  Bargaining; Welfarism; Nash; KalaiSmorodinsky; Expected Utility 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:bro:econwp:20095&r=gth 
By:  Kin Chung Lo (York University, Toronto) 
Abstract:  We generalize permissibility (Brandenburger, 1992) to allow for any suitably defined model of preference and definition of possibility. We also prove that the generalized solution concept characterizes rationality, caution, and “common belief" of rationality and caution. 
JEL:  C72 D81 
Date:  2009–09 
URL:  http://d.repec.org/n?u=RePEc:yca:wpaper:2009_01&r=gth 
By:  Choi, Kangsik 
Abstract:  This study investigates social welfare and privatization depending on the government's preference for tax revenues and the timing of wage setting in either a unionizedmixed or a unionizedprivatized duopolistic market. We show that bargaining over wages is always sequential regardless of who decide the timing of endogenous wage setting and market type except for the following cases; (i) there cannot be any sustained equilibrium or (ii) any timing can be sustained as an equilibrium. Moreover, if the government's preference for tax revenues is sufficiently large, the privatization of the public firm is harmful in terms of both social welfare and government's payoff whether the wage setting is simultaneous or not. However, if the government's preference for tax revenues is sufficiently small, there can exist incongruence regarding privatization between the public firm and the government. 
Keywords:  Endogenous Wage Setting; Government's Preference; Social Welfare; Tax; Privatization. 
JEL:  C79 L13 J51 D43 L33 H44 
Date:  2009–09–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:17221&r=gth 