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on Game Theory |
| By: | Itai Ashlagi (Harvard Business School, Negotiation, Organizations & Markets Unit); Emin Karagozoglu (Department of Economics, Maastricht University); Bettina Klaus (Harvard Business School, Negotiation, Organizations & Markets Unit) |
| Abstract: | We consider estate division problems, a generalization of bankruptcy problems. We show that in a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal division. Next, we consider division rules satisfying efficiency, equal treatment of equals, and claims monotonicity. For claim games with at most three agents, again all Nash equilibria induce equal division. Surprisingly, this result does not extend to claim games with more than three agents. However, if nonbossiness is added, then equal division is restored. |
| Keywords: | Bankruptcy/estate division problems, claims monotonicity, direct revelation claim game, equal division, equal treatment of equals, Nash equilibria, nonbossiness, (weak) order preservation. |
| JEL: | C72 D63 D71 |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:09-069&r=gth |
| By: | Nicholas Ziros |
| Abstract: | We present the bargaining set of an economy, where trades among groups of individuals are conducted via the Shapley-Shubik mechanism. Then we prove that in atomless economies the allocations resulting from this equilibrium notion are competitive. |
| Keywords: | Strategic market games, Bargaining set, Competition |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:ucy:cypeua:8-2008&r=gth |
| By: | Fabien Lange (Budapest Tech); Michel Grabisch (Centre d’Economie de la Sorbonne) |
| Abstract: | In cooperative game theory, the Shapley value is a central notion defining a rational way to share the total worth of a game among players. In this paper, we address a general framework leading to applications to games with communication graphs, where the set of feasible coalitions forms a poset where all maximal chains have the same length. We first show that previous definitions and axiomatizations of the Shapley value proprosed by Faigle and Kern, and Bilbao and Edelman still work. Our main contribution is then to propose a new axiomatization avoiding the hierarchical strength axiom of Faigle and Kern, and considering a new way to define the symmetry among players. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the classical efficiency axiom correspond actually to the two Kirchhoff’s laws in the resistor circuit associated to the Hasse diagram of feasible coalitions. We finally work out a weak form of the monotonicity axiom which is satisfied by the proposed value. |
| Keywords: | Regular set systems; regular games; Shapley value; probabilistic efficient values; regular values; Kirchhoff’s laws. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:0807&r=gth |
| By: | Julien Reynaud (European Central Bank); Fabien Lange (Budapest Tech); Lukasz Gatarek (European Central Bank); Christian Thimann (European Central Bank) |
| Abstract: | Voting power methodology offers insights to understand coalition building in collective decision making. This paper proposes a new measure of voting power inspired from Banzhaf (1965) accounting for the proximity between voters by capturing how often they appear in winning coalitions together. Using this proximity index, we introduce a notion of relative linkages among coalition participants as determinant of coalition building. We propose an application to the governance structure of the International Monetary Fund, with linkages being represented by bilateral volumes of trade between voters. The results are able to explain several important features of the functioning of this particular voting body, and may be useful for other applications in international politics. |
| Keywords: | voting power index, coalition building, International Monetary Fund, linkage, proximity |
| JEL: | C71 F33 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:0808&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 - 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 - CNRS : UMR6579) |
| Abstract: | This article explores individual incentives to produce information on communication networks. In our setting, efforts are strategic complements along communication paths with convex decay. We analyze Nash equilibria on a set of networks which are unambiguous in terms of centrality. We first characterize both dominant and dominated equilibria. Second, we examine the issue of social coordination in order to reduce the social dilemma. |
| Keywords: | Communication Network, Endogenous Efforts, Strategic Complements |
| Date: | 2008–11–17 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00339159_v1&r=gth |
| By: | Dimitri Dubois; Marc Willinger; Phu Nguyen Van |
| Abstract: | We compare the experimental results of three stag-hunt games. In contrast to Battalio et al. (2001), our design keeps the riskiness ratio of the payoff-dominant and the risk-dominant strategies at a constant level as the optimisation premium is increased. We define the riskiness ratio as the relative payoff range of the two strategies. We find that decreasing the riskiness ratio while keeping the optimization premium constant increases sharply the frequency of the risk-dominant strategy. On the other hand an increase of the optimization premium with a constant riskiness ratio has no effect on the choice frequencies. Finally, we confirm the dynamic properties found by Battalio et al. that increasing the optimization premium favours best-response and sensitivity to the history of play. |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:08-19&r=gth |
| By: | Kumabe, Masahiro; Mihara, H. Reiju |
| Abstract: | Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from the agenda all the alternatives that are non-maximal for all players in a winning coalition. Unlike the core, the core without majority dissatisfaction depends only onthe players' sets of maximal elements and is included in the union of such sets. A result for an extended framework gives another sense in which the core without majority dissatisfaction behaves better than the core. |
| Keywords: | Core; Nakamura number; kappa number; simple games; voting games; maximal elements; acyclic preferences; limit ordinals |
| JEL: | D71 C71 C02 |
| Date: | 2008–11–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11728&r=gth |
| By: | Subhasish Dugar; Haimanti Bhattacharya |
| Abstract: | This paper presents an experimental investigation of how a systematic variation in the cognitive demands on subjects affects the optimal play. The innovation of this paper is the choice of a game, which we call the Game of Position. This is a two-player zero-sum game characterized by a dominant-strategy solution that involves iterative steps of reasoning. The equilibrium play is independent of mutual beliefs of players; hence inability of a subject to play the dominant-strategy unambiguously implies the failure of human reasoning prowess. We alter the two parameters of the game to vary the cognitive constraints, as represented by these steps of reasoning, on players. Our main substantive conclusion is that the frequency of the dominant-strategy play sharply increases as we limit the cognitive demands on players. |
| Keywords: | Non-cooperative game theory, cognition, laboratory experiment |
| JEL: | C72 D83 C91 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:uta:papers:2008_20&r=gth |
| By: | Topi Miettinen (SITE, Stockholm School of Economics, and Max Planck Institute for Ecopnomics, Jena, Germany) |
| Abstract: | In line with the widely applied principle of just deserts, we assume that the severity of the penalty on a contract offender increases in the harm on the other. When this principle holds, the influence of the efficiency of the agreement on the incentives to abide by it crucially depends on whether actions are strategic complements or substitutes. With strategic substitutes, there is a conflict between Pareto-efficiency and the incentives to abide. The opposite tends to be true when actions are strategic complements. The results are interpreted in the context of legal contracts and in that of informal mutual promises. |
| Keywords: | partnerships, contracts, pre-play communication, legal enforcement, social norms, guilt |
| JEL: | C72 C78 K12 Z13 |
| Date: | 2008–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2008-088&r=gth |
| By: | Basuchoudhary, Atin; Allen, Sam; Siemers, Troy |
| Abstract: | We model an assurance game played within a population with two types of individuals -- short-sighted and foresighted. Foresighted people have a lower discount rate than short sighted people. These phenotypes interact with each other. We define the persistent interaction of foresighted people with other foresighted people as a critical element of civilization while the interaction of short sighted people with other short sighted people as critical to the failure of civilization. We show that whether the short sighted phenotype will be an evolutionary stable strategy (and thus lead to the collapse of civilization) depends on the initial proportion of short sighted people relative to people with foresight as well as their relative discount rates. Further we explore some comparative static results that connect the probability of the game continuing and the relative size of the two discount rates to the likelihood that civilization will collapse. |
| Keywords: | society; breakdown; evolution; replicator; dynamic; process; civilization; conflict; institution |
| JEL: | D02 N3 D83 C73 |
| Date: | 2008–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11765&r=gth |