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on Game Theory |
| By: | René van den Brink (VU University Amsterdam) |
| Abstract: | We consider cooperative transferable utility games, or simply TU-games, with a limited communication structure in which players can cooperate if and only if they are connected in the communication graph. A difference between the restricted Banzhaf value and the Myerson value (i.e. the Shapley value of the restricted game) is that the restricted Banzhaf value satisfies collusion neutrality, while the Myerson value satisfies component efficiency. Requiring both efficiency and collusion neutrality for cycle-free graph games yields other solutions such as the hierarchical outcomes and the average tree solution. Since these solutions also satisfy the superfluous player property, this also `solves' an impossibility for TU-games since there is no solution for these games that satisfies efficiency, collusion neutrality and the null player property. We give axiomatizations of the restricted Banzhaf value, the hierarchical outcomes and the average tree solution that are comparable with axiomatizations of the Myerson value in case the communication graph is cycle-free. Finally, we generalize these solutions to classes of solutions for cycle-free graph games using network power measures. |
| Keywords: | Cooperative TU-game; communication structure; Myerson value; Shapley value; Banzhaf value; hierarchical outcome; average tree solution; component efficiency; collusion neutrality. |
| JEL: | C71 |
| Date: | 2009–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20090108&r=gth |
| By: | Michel Grabisch (Université Paris I Panthéon-Sorbonne, Centre d'Economie de la Sorbonne, 106-112 Bd de l'Hôpital, 75013 Paris, France); Agnieszka Rusinowska (GATE, CNRS UMR 5824 - Université de Lyon, 93 Chemin des Mouilles - B.P. 167, 69131 Ecully Cedex, France) |
| Abstract: | In the paper, we generalize a two-action (yes-no) model of influence to a framework in which every player has a continuum of actions and he has to choose one of them. We assume the set of actions to be an interval. Each player has an inclination to choose one of the actions. Due to influence among players, the final decision of a player, i.e., his choice of one action, may be different from his original inclination. In particular, a coalition of players with the same inclination may influence another player with different inclination, and as a result of this influence, the decision of the player is closer to the inclination of the influencing coalition than his inclination was. We introduce and study a measure of such a positive influence of a coalition on a player. Several unanimous influence functions in this generalized framework are considered. Moreover, we investigate other tools for analyzing influence, like the concept of a follower of a given coalition, its particular case - a perfect follower, and the kernel of an influence function. We study properties of these concepts. Also the set of fixed points under a given influence function is analyzed. Furthermore, we study linear influence functions. We also introduce a measure of a negative influence of a coalition on a player. |
| Keywords: | action, decision, influence index, unanimous influence function, follower of a coalition, kernel, fixed point, linear influence function |
| JEL: | C7 D7 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1004&r=gth |
| By: | Igal Milchtaich (Department of Economics, Bar-Ilan University) |
| Abstract: | Every finite noncooperative game can be presented as a weighted network congestion game, and also as a network congestion game with player-specific costs. In the first presentation, different players may contribute differently to congestion, and in the second, they are differently (negatively) affected by it. This paper shows that the topology of the underlying (undirected two-terminal) network provides information about the existence of pure-strategy Nash equilibrium in the game. For some networks, but not for others, every corresponding game has at least one such equilibrium. For the weighted presentation, a complete characterization of the networks with this property is given. The necessary and sufficient condition is that the network has at most three routes that do traverse any edge in opposite directions, or it consists of several such networks connected in series. The corresponding problem for player-specific costs remains open. |
| Keywords: | Congestion games, network topology, existence of equilibrium |
| JEL: | C72 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:biu:wpaper:2010-09&r=gth |
| By: | Anders Poulsen (School of Economics, University of East Anglia); Michael Roos (Ruhr-Universitaet Bochum; School of Economics, University of East Anglia) |
| Abstract: | Game theory predicts that players make strategic commitments that may appear counter-intuitive. We conducted an experiment to see if people make a counter-intuitive but strategically optimal decision to avoid information. The experiment is based on a sequential Nash demand game in which a responding player can commit ahead of the game not to see what a proposing player demanded. Our data show that subjects do, but only after substantial time, learn to make the optimal strategic commitment. We find only weak evidence of physical timing effects. |
| Keywords: | Strategic commitment, commitment, bargaining, strategic value of information, physical timing effects, endogenous timing, experiment |
| JEL: | J3 J6 M5 |
| Date: | 2010–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:uea:aepppr:2010_07&r=gth |
| By: | Tadenuma, Koichi |
| Abstract: | In two-sided matching problems, we consider “natural” changes in preferences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rankenhancements of partners. One property requires that an agent who becomes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the “irrelevant” agents, whose preferences as well as whose original partners’ preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold. |
| Keywords: | two-sided matching problem, stable matching, partnership, solidarity |
| JEL: | C78 C71 D71 D63 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2010-04&r=gth |
| By: | Nunez Matias (THEMA, Universite de Cergy-Pontoise) |
| Abstract: | Approval Voting is shown to be the unique scoring rule that leads strategic voters to sincere behavior of three candidates elections in Poisson Games. However, Approval Voting can lead to insincere behavior in elections with more than three candidates. |
| Keywords: | Sincerity, Approval Voting, Scoring rules, Poisson Games |
| JEL: | D72 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2010-02&r=gth |
| By: | Maurice Koster (University of Amsterdam); Ines Lindner (VU University Amsterdam); Gordon McCormick (NPS Monterey); Guillermo Owen (NPS Monterey) |
| Abstract: | We consider a game played by a state sponsor of terrorism, a terrorist group, and the target of terrorist attacks. The sponsoring state wishes to see as much damage inflicted on the target of attack as possible, but wishes to avoid retaliation. To do so, his relationship with the terrorist group must remain ambiguous. The target of attack, for his part, wishes to bring these attacks to an end as quickly as possible and will consider the option of retaliating against the sponsor to do so. We approach the problem by introducing an “evidence” variable in a dynamic setting. We show that the interplay of different strategic and non-strategic effects boils down to three qualitatively different scenarios, determined by key parameters. Based on this result, two alternative instruments to retaliation are identified in order to resist terrorist activities. First, assuming that the target is able to change some parameters by monetary investments, the paper provides an economic analysis of how to invest optimally in order to make the sponsor lose incentives to support the terrorist group. Second, we propose changing the structure of the game. Here, the key insight is that the target country can make a unilateral statement as to his strategy. The sponsor cannot do so as he is in fact claiming that there is no cooperation with terrorist groups. While our discussion, in this article, is motivated by an important problem in contemporary counterterrorism policy, it applies more generally to the study of secret coalitions. |
| Keywords: | Secret Coalitions; Security Economics; Noncooperative Games |
| JEL: | C72 D82 |
| Date: | 2010–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100001&r=gth |
| By: | Mohamed Belhaj (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579); Frédéric Deroïan (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579) |
| Abstract: | A set of agents is organized in a social network, which conveys synergies in two activities. Each agent has one unit of a resource to allocate between two activities. We show that individual choices are shaped by Bonacich centrality measures and an attractiveness multiplier. The latter, combined with the elasticity of Bonacich centrality with respect to the intensity of interaction, drives the sign of the network reaction to a modication of the costs of activities. |
| Keywords: | Social Network, Limited Resource, Competing Activities, Attractiveness Multiplier, Elasticity of Bonacich Centrality. |
| Date: | 2010–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00481460_v1&r=gth |
| By: | Arantza Estévez-Fernández (VU University Amsterdam) |
| Abstract: | This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If |
| Keywords: | Project planning; delay; expedition; cost sharing mechanism; surplus sharing mechanism; bankruptcy |
| JEL: | C71 C44 |
| Date: | 2009–10–20 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20090090&r=gth |
| By: | Maarten Janssen (University of Vienna, and Erasmus University Rotterdam); Vladimir A. Karamychev; Emiel Maasland (Erasmus School of Economics, Erasmus University Rotterdam) |
| Abstract: | There is by now a large literature arguing that auctions with a variety of after-market interactions may not yield an efficient allocation of the objects for sale, especially when the bidders impose strong negative externalities upon each other. This paper argues that these inefficiencies can be avoided by asking bidders prior to the auction to submit any public payment they would like to make. These payments, so-called flexible entry fees, do not affect the allocation decision of the auctioneer. We show that auctions with flexible entry fees have a fully revealing equilibrium where bidders signal their type before the auction itself takes place. |
| Keywords: | auctions; efficiency; entry fee; negative externality; revenue |
| JEL: | C72 D44 |
| Date: | 2009–11–30 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20090109&r=gth |