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on Game Theory |
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Issue of 2010‒01‒16
eighteen papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University |
| By: | Okada, Akira |
| Abstract: | We consider information transmission in the core of an exchange economy with incomplete information by non-cooperative bargaining theory. Reformulating the coalitional voting game by Serrano and Vohra [Information transmission in coalitional voting games, J. of Economic Theory (2007), 117-137] so that an informed agent proposes an allocation, we define a notion of the informational core. A coalition has an informational objection to the status-quo allocation if and only if there exists an equilibrium rejection in the coalitional voting game. We present a non-cooperative sequential bargaining game in which coalitional voting games are repeated, and prove that a refinement of a sequential equilibrium of the bargaining game necessarily yields an allocation in the informational core. |
| Keywords: | core, exchange economy, incomplete information, information transmission, non-cooperative bargaining |
| JEL: | C71 C72 D51 D82 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2009-16&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results. |
| Keywords: | TU-game; solution concept; core; feasible coalition; communication graph; partially ordered set |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00445171_v1&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Agnieszka Rusinowska (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines) |
| Abstract: | In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. Some of the presented influence functions are equivalent to the command games, that is, they are compatible with the command games, and additionally each follower of a coalition under the command influence function is also a commandable player for that coalition in the command games. For some influence functions we define the equivalent command games. We show that not for all influence functions the compatible command games exist. Moreover, we propose a more general definition of the influence index and show that under some assumptions, some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. Both the Shapley-Shubik index and the Banzhaf index are equal to a difference between the weighted influence indices under some influence functions, and the only difference between these two power indices lies in the weights for the influence indices. An example of the Confucian model of society is broadly examined. |
| Keywords: | influence function; follower; influence index; command game; commandable player; Shapley-Shubik index; Banzhaf index |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00445126_v1&r=gth |
| By: | Giuseppe De Marco (Università di Napoli Parthenope); Jacqueline Morgan (Università di Napoli Federico II and CSEf) |
| Abstract: | The famous Harsanyi's (1973) Theorem states that generically a finite game has an odd number of Nash equilibria in mixed strategies. In this paper, we show that for finite multicriteria games (games with vector-valued payoffs) this kind of result does not hold. In particular, we show, by examples, that it is possible to find balls in the space of games such that every game in this set has uncountably many equilibria so that uncountable sets of equilibria are not nongeneric in multicriteria games. Moreover, we point out that, surprisingly, all the equilibria of the games cor- responding to the center of these balls are essential, that is, they are stable with respect to every possible perturbation on the data of the game. However, if we consider the scalarization stable equilibrium concept (introduced in De Marco and Morgan (2007) and which is based on the scalarization technique for multicriteria games), then we show that it provides an effective selection device for the equilibria of the games corresponding to the centers of the balls. This means that the scalarization stable equilibrium concept can provide a sharper selection device with respect to the other classical refinement concepts in multicriteria games. |
| Date: | 2009–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:242&r=gth |
| By: | John Duffy; Felix Munoz-Garcia (School of Economic Sciences, Washington State University) |
| Abstract: | This paper investigates how the introduction of social preferences affects players’ equilibrium behavior in both one-shot and infinitely repeated versions of the Prisoner’s Dilemma game. We first show that defection survives as the unique equilibrium of the stage game if at least one player is not too concerned about inequity aversion. Second, we demonstrate that in the infinitely repeated version of the game, fairness concerns operate as a “substitute: for time discounting, as fairness helps sustain cooperation for lower discount factors. We then extend our results to more general simultaneous-move games, and more general preferences. Furthermore, we examine how the introduction of incomplete information about players’ social preferences can help in the selection of the efficient cooperative outcome. Finally, we point out the implications of our findings for the design and analysis of experiments involving repeated games. In particular, repeated game equilibria which are thought to be supported by sufficiently large discount factors, may in fact be sustained by a combination of discounting and social preference parameters, an observation that may help rationalize recent experimental findings. |
| Keywords: | Prisoner’s dilemma; Repeated games; Inequity aversion; Time discounting; Time discounting; Social Preferences |
| JEL: | C72 C73 H43 D91 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:wsu:wpaper:munoz-4&r=gth |
| By: | Pedro Miranda (Universidad Complutense de Madrid - Department of Statistics and O.R.); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | In this paper we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of the game. Based on the concept of $k$-additivity, we define the so-called $k$-balanced games and the corresponding generalization of core, the $k$-additive core, whose elements are not directly imputations but $k$-additive games. We show that any game is $k$-balanced for a suitable choice of $k,$ so that the corresponding $k$-additive core is not empty. For the games in the $k$-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be $k$-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities. |
| Keywords: | Cooperative Games; k-additivity; balanced games; capacities; core |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00445073_v1&r=gth |
| By: | Johannes Horner (Cowles Foundation, Yale University); Takuo Sugaya (Princeton University); Satoru Takahashi (Princeton University); Nicolas Vieille (HEC Paris) |
| Abstract: | We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the state. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting. |
| Keywords: | Stochastic games |
| JEL: | C72 C73 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1742&r=gth |
| By: | Michael Finus (University of Stirling); Bianca Rundshagen (University of Hagen); Johan Eyckmans (atholieke Universiteit Leuven, Centrum voor Economische Studiën and Hogeschool-Universiteit Brussels) |
| Abstract: | We analyze stability of self-enforcing climate agreements based on a data set generated by the CLIMNEG world simulation model (CWSM), version 1.2. We consider two new aspects which appear important in actual treaty-making. First, we consider a sequential coalition formation process where players can make proposals which are either accepted or countered by other proposals. Second, we analyze whether a moderator, like an international organization, even without enforcement power, can improve upon globally suboptimal outcomes through coordinating actions by making recommendations that must be Pareto-improving to all parties. We discuss the conceptual difficulties of implementing our algorithm. |
| Keywords: | International Climate Agreements, Sequential Coalition Formation, Coordination through Moderator, Integrated Assessment Model, Algorithm for Computations |
| JEL: | C79 H87 Q54 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2009.109&r=gth |
| By: | Claudia Keser; Irina Suleymanova; Christian Wey |
| Abstract: | We analyze the choices between two technologies A and B that both exhibit network effects. We introduce a critical mass game in which coordination on either one of the standards constitutes a Nash equilibrium outcome while coordination on standard B is assumed to be payoff-dominant. We present a heuristic definition of a critical mass and show that the critical mass is inversely related to the mixed strategy equilibrium. We show that the critical mass is closely related to the risk dominance criterion, the global game theory, and the maximin criterion. We present experimental evidence that both the relative degree of payoff dominance and risk dominance explain players' choices. We finally show that users' adoption behavior induces firms to select a relatively unrisky technology which minimizes the problem of coordination failure to the benefit of consumers. |
| JEL: | C72 C91 D91 D84 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp961&r=gth |
| By: | Reinoud Joosten |
| Abstract: | We present two new notions of evolutionary stability, the truly evolutionarily stable state (TESS) and the generalized evolutionarily stable equilibrium (GESE). The GESE generalizes the evolutionarily stable equilibrium (ESE) of Joosten [1996]. An ESE attracts all nearby trajectories monotonically, i.e., the Euclidean distance decreasing steadily in time. For a GESE this property should holds for at least one metric. The TESS generalizes the evolutionarily stable strategy (ESS) of Maynard Smith & Price [1973]. A TESS attracts nearby trajectories too, but the behavior of the dynamics nearby must be similar to the behavior of the replicator dynamics near an ESS. Both notions are defned on the dynamics and immediately imply asymptotical stability for the dynamics at hand, i.e., the equilibrium attracts all trajectories sufficiently nearby. We consider this the relevant and conceptually right approach in defining evolutionary equilibria, rather than defining a static equilibrium notion and search for appropriate dynamics guaranteeing its dynamic stability. Moreover, the GESE and the TESS take similar positions as the ESE and ESE do in relation to other equilibrium and fixed point concepts in general. |
| Keywords: | evolutionary stability, evolutionary game theory Length 27 pages |
| JEL: | A12 C62 C72 C73 D83 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:esi:evopap:2009-16&r=gth |
| By: | Funk, Matt |
| Abstract: | This paper introduces a game-theoretical framework for The Problem of Sustainable Economic Development, axioms which help clarify the problem itself, and, reductio ad absurdum, falsify many widely-held economic, evolutionary, and ecological principles. This brief communiqué lays the foundation for evolutionary stable economic development and survival strategies – strategies which foster international cooperation, global threat mitigation, food & energy security, long-distance dispersibility, and thus, ultimately, the long-term survival of the human species. |
| Keywords: | sustainable economic development; tragedy of the commons; noncooperative games; natural selection; global threats; food security; national security; human survival |
| JEL: | B40 Q57 C72 |
| Date: | 2009–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19442&r=gth |
| By: | de Marti, Joan (Universitat Pompeu Fabra); Zenou, Yves (Research Institute of Industrial Economics (IFN)) |
| Abstract: | We survey the literature on social networks by putting together the economics, sociological and physics/applied mathematics approaches, showing their similarities and differences. We expose, in particular, the two main ways of modeling network formation. While the physics/applied mathematics approach is capable of reproducing most observed networks, it does not explain why they emerge. On the contrary, the economics approach is very precise in explaining why networks emerge but does a poor job in matching real-world networks. We also analyze behaviors on networks, which take networks as given and focus on the impact of their structure on individuals’ outcomes. Using a game-theoretical framework, we then compare the results with those obtained in sociology. |
| Keywords: | Random Graph; Game Theory; Centrality Measures; Network Formation; Weak |
| JEL: | A14 C72 D85 Z13 |
| Date: | 2009–12–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:iuiwop:0816&r=gth |
| By: | Alain Chateauneuf (Centre d'Economie de la Sorbonne); Caroline Ventura (Centre d'Economie de la Sorbonne) |
| Abstract: | This paper is concerned with real valued set functions defined on the set of Borel sets of a locally compact ?-compact topological space ?. The first part characterizes the strong and weak impatience in the context of discrete and continuous time flows of income (consumption) valued through a Choquet integral with respect to an (exact) capacity. We show that the impatience of the decision maker translates into continuity properties of the capacity. In the second part, we recall the generalization given by Rébillé [8] of the Yosida-Hewitt decomposition of an additive set function into a continuous part and a pathological part and use it to give a characterization of those convex capacities whose core contains at least one G-continuous measure. We then proceed to characterize the exact capacities whose core contains only G-continuous measures. As a dividend, a simple characterization of countably additive Borel probabilities on locally compact ?-compact metric spaces is obtained. |
| Keywords: | Impatience, exact and convex capacities,G-cores, ?cores, Yosida-Hewitt decomposition. |
| JEL: | D81 |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09081&r=gth |
| By: | Demange, Gabrielle (Paris School of Economics (EHESS)); Van Der Straeten, Karine (Toulouse School of Economics) |
| Abstract: | This paper proposes a game to study strategic communication on platforms by parties. Parties’ platforms have been chosen in a multidimensional policy space, but are imperfectly known by voters. Parties strategically decide the emphasis they put on the various issues, and thus the precision of the information they convey to voters on their position on each issue. The questions we address are the following: what are the equilibria of this communication game? How many issues will they address? Will parties talk about the same issues or not? Will they talk on issues that they "own" or not? |
| JEL: | C70 D70 |
| Date: | 2009–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:ide:wpaper:21675&r=gth |
| By: | Swee-Hoon Chuah (Nottingham University Business School) |
| Abstract: | In contrast to current literature which mainly identifies relationships between particular economic behaviours and specific attitudes suggestive of those behaviours, we explore the potential of general human values for explaining economic behaviour. In particular, we investigate whether behaviours observed in binary-choice lotteries, time discounting, public good, ultimatum, dictator and trust game experiments can be explained by Schwartz’s theory of universal human values. We find that the values have explanatory power in relation to strategic, but not parametric, behaviours. We discuss this finding in terms of the sociology of values and suggest that situations involving human interactions provide the most conducive context for the expression of values. We also find that different subsets of the values relate to different strategic behaviours, indicating that there is no redundancy in their explanatory power. |
| Keywords: | Values, behaviour, survey, experiments |
| JEL: | C72 C91 D81 |
| Date: | 2010–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:bbr:workpa:6&r=gth |
| By: | Enrico Guzzini; Antonio Palastrini |
| Abstract: | In this paper, we consider the Coase theorem in a non cooperative game framework. In particular, we explore the robustness of the Coase theorem with respect to the ?nal distribution of alienable property rights which constitutes, as far as we know, a less cultivated ?eld of research. In our framework, in order to reach e¢ ciency, agents have to stipulate binding contracts. In the analysis, we distinguish between permanent and temporary contracts showing the di¤erent implication of the two kinds of contracts with respect to the ?nal attribution of individual rights. More precisely, we show that, with temporary binding contracts and under particular assumptions, the ?nal attribution if individual rights does not converge. |
| Keywords: | Coase theorem, binding contracts, side payments |
| JEL: | C7 D6 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:ter:wpaper:0060&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University); Olivier Tercieux (Paris School of Economics) |
| Abstract: | We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict (and thus stronger) version of the monotonicity condition introduced by Maskin (1999) is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive (i.e., it never selects the same outcome in two distinct states), we show that it is also sufficient under a mild "no worst alternative" condition. In particular, no economic condition is required. We also discuss how our results extend when the social choice function is not responsive. |
| Keywords: | Implementation, Complete information, Rationalizability, Maskin monotonicity |
| JEL: | C79 D82 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1697r&r=gth |
| By: | Francesconi, Marco (University of Essex); Ghiglino, Christian (University of Essex); Perry, Motty (Hebrew University, Jerusalem) |
| Abstract: | This paper presents an overlapping generations model to explain why humans live in families rather than in other pair groupings. Since most non-human species are not familial, something special must be behind the family. It is shown that the two necessary features that explain the origin of the family are given by uncertain paternity and overlapping cohorts of dependent children. With such two features built into our model, and under the assumption that individuals care only for the propagation of their own genes, our analysis indicates that fidelity families dominate promiscuous pair bonding, in the sense that they can achieve greater survivorship and enhanced genetic fitness. The explanation lies in the free riding behavior that characterizes the interactions between competing fathers in the same promiscuous pair grouping. Kin ties could also be related to the emergence of the family. When we consider a kinship system in which an adult male transfers resources not just to his offspring but also to his younger siblings, we find that kin ties never emerge as an equilibrium outcome in a promiscuous environment. In a fidelity family environment, instead, kinship can occur in equilibrium and, when it does, it is efficiency enhancing in terms of greater survivorship and fitness. The model can also be used to shed light on the issue as to why virtually all major world religions are centered around the importance of the family. |
| Keywords: | fatherhood uncertainty, free riding, kinship systems, religion, overlapping generations, divorce and blended families |
| JEL: | C72 D01 D10 J12 Z13 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp4637&r=gth |