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on Game Theory |
| By: | Kongo, T.; Funaki, Y.; Tijs, S.H. (Tilburg University, Center for Economic Research) |
| Abstract: | Some new axiomatic characterizations and recursive formulas of the Shapley value are presented. In the results, dual games and the self-duality of the value implicitly play an important role. A set of non-cooperative games which implement the Shapley value on the class of all games is given. |
| Keywords: | Shapley value;axiomatization;implementation |
| JEL: | C71 C72 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200790&r=gth |
| By: | Jacques Durieu (CREUSET (EA 3724) - Centre de Recherche Economique de l'Université de Saint Etienne - Université Jean Monnet - Saint-Etienne); Hans Haller (Department of economics - Virginia Polytechnic Institute and State University); Nicolas Quérou (School of Management and Economics - Queen's University of Belfast); Philippe Solal (CREUSET (EA 3724) - Centre de Recherche Economique de l'Université de Saint Etienne - Université Jean Monnet - Saint-Etienne) |
| Abstract: | We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we ex- tend Voorneveld's concept of best-response potential from cardinal to ordi- nal games and derive the analogue of his characterization result: An ordi- nal game is a best-response potential game if and only if it does not have a best-response cycle. Further, Milgrom and Shannon's concept of quasi- supermodularity is extended from cardinal games to ordinal games. We ¯nd that under certain compactness and semicontinuity assumptions, the ordinal Nash equilibria of a quasi-supermodular game form a nonempty complete lattice. Finally, we extend several set-valued solution concepts from cardinal to ordinal games in our sense. |
| Keywords: | Ordinal Games, Potential Games, Quasi-Supermodularity, Rationalizable Sets, Sets Closed under Behavior Correspondences |
| Date: | 2007–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:ujm-00194794_v1&r=gth |
| By: | Funaki, Y.; Yamato, T. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper, we examine the question of which coalition structures farsighted players form in coalition formation games with externalities. We introduce a stability concept for a coalition structure called a sequentially stable coalition structure. Our concept of domination between two coalition structures is based on a ?step-by-step? approach to describe negotiation steps concretely by restricting how coalition structures can change: when one coalition structure is changed to another one, either (i) only one merging of two separate coalitions into a coalition occurs, or (ii) only one breaking up of a coalition into two separate coalitions happens. As applications of our stability notion, we show that the efficient grand coalition structure can be sequentially stable in simple partition function form games and common pool resource games. |
| JEL: | C70 C71 D62 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200796&r=gth |
| By: | Funaki, Y.; Tijs, S.H.; Branzei, R. (Tilburg University, Center for Economic Research) |
| Abstract: | The lexicographic vectors of a balanced game, called here leximals, are used to define a new solution concept, the lexicore, on the cone of balanced games. Properties of the lexicore and its relation with the core on some classes of games are studied. It is shown that on cones of balanced games where the core is additive, the leximals, the lexicore and the Average Lexicographic (AL-)value are additive, too. Further, it turns out that the leximals satisfy a consistency property with respect to a reduced game `a la Davis and Maschler, which implies an average consistency property of the AL-value. Explicit formulas for the AL-value on the class of k-convex games and on the class of balanced almost convex games are provided. |
| Keywords: | cooperative games;the core;the AL-value;the Shapley value |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200797&r=gth |
| By: | Lotito, Gianna |
| Abstract: | The purpose of this paper is that of extending the model of Resolute Choice (McClennen 1990) to a situation of interaction and comparing its performance with the Sophisticated-subgame perfect equilibrium model in an experiment. A non-cooperative game in which two players with different preference orderings over outcomes move sequentially is adopted as a framework to compare the two models. I consider those combinations of the players' preference structures which generate the different plans and find those game situations where either one or two outcomes Pareto-dominant over Sophisticated Choice exist. Two definitions of Resolute Choice are therefore tested, which allow to discriminate choice between two different Pareto dominant outcomes. In the experiment three games with the same structure but different payoffs are played. The design allows preliminary group discussion among the players about the decisions to be taken, which is taped and transcribed. The results show support for Resolute Choice as Pareto dominance, while the ability of Resolute Choice as Nash bargaining to explain behaviour is quite limited. The subjects' motivations are very useful in interpreting the results. They show that choice for a Pareto dominant outcome is mainly driven by the idea of Pareto optimality itself. Motivations differ slightly according to which strategy is chosen to reach one of the Pareto dominant outcomes. A result to be noted is the relevance of the different payoffs of the games in motivating choice. The method used in the experiment to elicit the subjects' responses is the strategy method. A direct consequence is that the results are all in terms of strategies chosen by subjects. In view of this, an alternative way to look at the experiment results has been tried, which consists in a simulation of the outcomes of the games that would have resulted from direct interaction among the players. The results have then been compared to the ones from the experiment. |
| Keywords: | dynamic decision making, myopia, sophistication, resoluteness, non-cooperative game |
| JEL: | C91 C72 D80 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:uca:ucapdv:94&r=gth |
| By: | Eric Maskin (School of Social Science, Institute for Advanced Study) |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:ads:wpaper:0080&r=gth |
| By: | Marcin Dziubinski; Debabrata Datta; Jaideep Roy |
| Abstract: | Two players are endowed with resources for setting up N locations on K identical circles, with N > K>= 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. They face a resource mobility constraint such that not all N locations can be placed in the rst round. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that for K = 1, the second mover always has a winning strategy in this game. In this paper we show that with K > 1, the second mover advantage disappears as in this case both players have a tying strategy. We also study a natural variant of this game where the resource mobility constraint is more stringent so that in each round each player chooses a single location where we show that the second mover advantage re-appears. We suggest some Nash equilibrium configurations of locations in both versions of the game. |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:edb:cedidp:07-15&r=gth |
| By: | Sascha Füllbrunn (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg) |
| Abstract: | In simultaneous ascending price auctions with heterogeneous goods Brusco and Lopomo (2002) derive collusive equilibria where bidders divide objects among themselves, while keeping the prices low. Considering a simultaneous ascending price auction with a fixed deadline, i.e. the Hard Close auction format, a prisoner’s dilemma situation results and collusive equilibria no longer exists, even for only two bidders. Hence, we introduce a further reason for sniping behavior in Hard Close auctions. |
| Keywords: | collusion, sniping, multi unit auctions, prisoner’s dilemma |
| JEL: | D44 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:mag:wpaper:07025&r=gth |
| By: | Marcin Dziubinski; Jaideep Roy |
| Abstract: | The paper studies an evolutionary model where players from a given population are randomly matched in pairs each period to play a co-ordination game. At each instant, a player can choose to adopt one of the two possible behavior rules, called the rational rule and the aspiring rule, and then take actions prescribed by the chosen rule. The choice between the two rules depends upon their relative performance in the immediate past. We show that there are two stable long run outcomes where either the rational rule becomes extinct and all players in the population achieve full eciency, or that both the behavior rules co-exist and there is only a partial use of ecient strategies in the population. These ndings support the use of the aspiration driven behavior in several existing studies and also help us take a comparative evolutionary look at the two rules in retrospect. |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:edb:cedidp:07-14&r=gth |
| By: | Dhaene G.; Bouckaert J. |
| Abstract: | We experimentally test Dufwenberg and Kirchsteiger’s (2004) theory of sequential reciprocity in a sequential prisoner’s dilemma (SPD) and a mini-ultimatum game (MUG). Data on subjects’ behavior and first and second-order beliefs allow us to classify their behavior as a material best response, a reciprocity best response, both, or none. In both games, about 80% of the first-movers’ behavior is a material best response, a reciprocity best response, or both. The remaining 20% of first-movers almost always make choices that are “too kind” according to the theory of reciprocity. Second-movers’ behavior, in both games, is fully in line with the predictions of the theory. Average behavior and beliefs, across subjects, are found to be compatible with a sequential reciprocity equilibrium in the SPD, but not in the MUG. We also found first- and second-order beliefs to be unbiased in the SPD, and nearly unbiased in the MUG, with the exception that first-movers in the MUG significantly overestimated the second-mover’s rejection rate of unequal offers. |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:ant:wpaper:2007026&r=gth |
| By: | Matias Nunez (LEEP - Laboratoire d'econometrie de l'école polytechnique - CNRS : UMR7657 - Polytechnique - X) |
| Abstract: | Approval voting features are analysed in a context of large elections with strategic voters: Myerson's Large Poisson Games. I first establish the Magnitude Equiva- lence Theorem (MET) which substantially reduces the complexity of computing the magnitudes of pivotal events. I also show that the Winner of the election coincides with the Profile Condorcet Winner at equilibrium when preferences are restricted to be single-peaked. This is a positive result that strengthens the positive conclusions some scholars have previously drawn over this voting rule. I finally show that, with- out the previous restriction over preferences, both concepts do not generally coincide anymore. |
| Date: | 2007–11–28 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:hal-00192488_v1&r=gth |
| By: | Claudia Keser; Claude Montmarquette |
| Abstract: | In a series of experimental games, each of two players may choose between remuneration based on either private or team effort. Although at least one of the players has the subgame perfect equilibrium strategy to choose remuneration based on private effort, we frequently observe team remuneration chosen by both players. Team remuneration allows for high payoff for each player for cooperation, but at the same time provides individual incentives to take a free ride on the other player's effort. Due to significant cooperation we observe that in team remuneration participants make higher profits than in private remuneration. We also observe that, when participants are not given the option of private remuneration, they cooperate significantly less. |
| Keywords: | Team effort, voluntary collaboration, experimental economics |
| JEL: | C72 C90 H41 J33 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp745&r=gth |