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on Game Theory |
| By: | Jingang Zhao (University of Saskatchewan) |
| Abstract: | This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then provides answers to the questions of what payoffs to split, how to split the payoff, what coalitions to form, and how long each of the coalitions will be formed by rational players in coalitional TU games. Finally, it obtains analogous results in coalitional NTU (non-transferable utility) games. |
| Keywords: | Coalition Formation, Core, Maximal Payoff, Minimum No-Blocking Payoff |
| JEL: | C62 C71 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.27&r=gth |
| By: | Dinko Dimitrov (University of Bayreuth); Emiliya Lazarova (School of Management and Economics, Queen’s University Belfast) |
| Abstract: | A coalitional matching is a two-sided matching problem in which agents on each side of the market may form coalitions such as student groups and research teams who - when matched - form universities. We assume that each researcher has preferences over the research teams he would like to work in and over the student groups he would like to teach to. Correspondingly, each student has preferences over the groups of students he wants to study with and over the teams of researchers he would like to learn from. In this setup, we examine how the existence of core stable partitions on the distinct market sides, the restriction of agents’ preferences over groups to strict orderings, and the extent to which individual preferences respect common rankings shape the existence of core stable coalitional matchings. |
| Keywords: | Coalitions, Common Rankings, Core, Stability, Totally Balanced Games, Two-Sided Matchings |
| JEL: | C78 J41 D71 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.45&r=gth |
| By: | Sergiu Hart; Andreu Mas-Colell |
| Abstract: | In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable. |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp484&r=gth |
| By: | Vincent Vannetelbosch (CORE University of Louvain); Ana Mauleon (CORE, University of Louvain); Wouter Vergote (CEREC, Facultés Universitaires Saint-Louis, and CORE, University of Louvain) |
| Abstract: | We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the von Neumann-Morgenstern (myopically) stable sets, von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many- to-one matching problems with responsive preferences. |
| Keywords: | Matching Problem, von Neumann-Morgenstern Stable Sets, Farsighted Stability |
| JEL: | C71 C78 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.29&r=gth |
| By: | Hideo Konishi (Boston College); Taiji Furusawa (Hitotsubashi University) |
| Abstract: | We consider a two-stage public goods provision game: In the first stage, players simultaneously decide if they will join a contribution group or not. In the second stage, players in the contribution group simultaneously offer contribution schemes in order to influence the government’s choice on the level of provision of public goods. Using perfectly coalition-proof Nash equilibrium (Bernheim, Peleg and Whinston, 1987 JET), we show that the set of equilibrium outcomes is equivalent to an "intuitive" hybrid solution concept, the free-riding-proof core, which is always nonempty but does not necessarily achieve global efficiency. It is not necessarily true that an equilibrium lobby group is formed by the players with highest willingness-to-pay, nor is it a consecutive group with respect to their willingnesses-to-pay. We also show that the equilibrium level of public goods provision shrinks to zero as the economy is replicated. |
| Keywords: | Common Agency, Public Good, Free Rider, Core, Lobby, Coalition Formation, Coalition-proof Nash Equilibrium |
| JEL: | C71 C72 F13 H41 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.23&r=gth |
| By: | Jürgen Eichberger (University of Heidelberg, Department of Economics); Dmitri Vinogradov (University of Essex, Essex Business School,) |
| Abstract: | Least-Unmatched Price Auctions have become a popular format of TV and radio shows. Increasingly, they are also applied in internet trading. In these auctions the lowest single (unique) bid wins. We analyze the game-theoretic solution of least unmatched price auctions when prize, bidding cost and the number of participants are known. We use a large data-set of such auctions in order to contrast actual behavior of players with game-theoretic predictions. In the aggregate, bidding behaviour seems to conform with a Nash equilibrium in mixed strategies. |
| Keywords: | games, experiments |
| JEL: | C71 C93 D01 D81 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0471&r=gth |
| By: | Markus Kinateder (Universitat Autònoma de Barcelona) |
| Abstract: | Delayed perfect monitoring in an infinitely repeated discounted game is modelled by allocating the players to a connected and undirected network. Players observe their immediate neighbors’ behavior only, but communicate over time the repeated game’s history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. Due to this and the bilateral communication structure, truthful communication arises endogenously only under additional conditions. The model also produces a network result; namely, the level of cooperation in this setup depends on the network’s diameter, and not on its clustering coefficient as in other models. |
| Keywords: | Repeated Game, Delayed Perfect Monitoring, Network, Communication |
| JEL: | C72 C73 D85 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.22&r=gth |
| By: | George J. Mailath (Department of Economics); : Wojciech Olszewski (Department of Economics, Northwestern University) |
| Abstract: | A strategy profile in a repeated game has bounded recall L if play under the profile after two distinct histories that agree in the last L periods is equal. Mailath and Morris (2002, 2006) proved that any strict equilibrium in bounded-recall strategies of a game with full support public monitoring is robust to all perturbations of the monitoring structure towards private monitoring (the case of almost-public monitoring), while strict equilibria in unbounded-recall strategies are typically not robust. We prove the perfect-monitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. As a consequence, the perfect monitoring folk theorem is shown to be behaviorally robust under almost-perfect almost-public monitoring. That is, the same specification of behavior continues to be an equilibrium when the monitoring is perturbed from perfect to highly-correlated private. |
| Keywords: | Repeated games, bounded recall strategies, folk theorem, imperfect monitoring |
| JEL: | C72 C73 |
| Date: | 2008–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-027&r=gth |
| By: | Rahmi Ilkiliç (Maastricht University) |
| Abstract: | A tragedy of the commons appears when the users of a common resource have incentives to exploit it more than the socially efficient level. We analyze the situation when the tragedy of the commons is embedded in a network of users and sources. Users play a game of extractions, where they decide how much resource to draw from each source they are connected to. We show that if the value of the resource to the users is linear, then each resource exhibits an isolated problem. There exists a unique equilibrium. But when the users have concave values, the network structure matters. The exploitation at each source depends on the centrality of the links connecting the source to the users. The equilibrium is unique and we provide a formula which expresses the quantities at an equilibrium as a function of a network centrality measure. Next we characterize the efficient levels of extractions by users and outflows from sources. Again, the case of linear values can be broken down source by source. For the case of concave values, we provide a graph decomposition which divides the network into regions according to the availability of sources. Then the efficiency problem can be solved region by region. |
| Keywords: | Tragedy of The Commons, Networks, Nash Equilibrium, Efficiency, Centrality Measures |
| JEL: | C62 C72 D85 Q20 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.30&r=gth |
| By: | Shmuel Zamir |
| Abstract: | An encyclopedia article on games with incomplete information. Table of contents: 1. Definition of the subject and its importance. 2. Introduction: Modeling incomplete information. 3. Harsanyi’s model: The notion of type. 4. Aumann’s model. 5. Harsanyi’s model and the hierarchies of beliefs. 6. The Universal Belief Space. 7. Belief subspaces. 8. Consistent beliefs and Common prior. 9. Bayesian games and Bayesian equilibrium. 10. Bayesian equilibrium and Correlated equilibrium. 11. Concluding remarks and future directions. 12. Bibliography. |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp486&r=gth |
| By: | Michèle Breton (GERAD, CREF and HEC Montréal); Lucia Sbragia (GERAD and HEC Montréal); Georges Zaccour (GERAD and Chair in Game Theory & Management HEC Montréal) |
| Abstract: | In this paper we develop a model to analyze, in a dynamic framework, how countries join international environmental agreements (IEAs). In the model, where countries suffer from the same environmental damage as a result of the total global emissions, a non-signatory country decides its emissions by maximizing its own welfare, whereas a signatory country decides its emissions by maximizing the aggregate welfare of all signatory countries. Signatory countries are assumed to be able to punish the non-signatories at a cost. When countries decide on their pollution emissions they account for the evolution of the pollution over time. Moreover, we propose a mechanism to describe how countries reach a stable IEA. The model is able to capture situations with partial cooperation in an IEA stable over time. It also captures situations where all countries participate in a stable agreement, or situations where no stable agreement is feasible. When more than one possibility coexists, the long-term outcome of the game depends on the initial conditions (i.e. the size of the initial group of signatory countries and the pollution level). |
| Keywords: | International Environmental Agreements, Non-Cooperative Dynamic Game, Coalition Stability |
| JEL: | C73 Q53 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.33&r=gth |
| By: | Coralio Ballester (Department of Economics, University of Alicante.); Pablo Brañas-Garza (Department of Economic Theory and Economic History, University of Granada.); María Paz Espinosa (Universidad del País Vasco) |
| Abstract: | This paper analyzes the impact of social integration on cooperative behavior. We show that if the social network shows assortative mixing then conditional cooperation is an equilibrium strategy for altruistic subjects with a high degree of social integration.We provide experimental evidence on the relationship between individuals’ position in a social network and their contributions in a public good game. |
| Keywords: | public good game, social networks, conditional cooperation. |
| JEL: | C91 D64 C72 H41 |
| Date: | 2008–06–27 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:08/04&r=gth |
| By: | Andrew Dowell (University of Liverpool); Michael Wooldridge (University of Liverpool); Peter McBurney (University of Liverpool) |
| Abstract: | Qualitative coalitional games (QCG) are representations of coalitional games in which self interested agents, each with their own individual goals, group together in order to achieve a set of goals which satisfy all the agents within that group. In such a representation, it is the strategy of the agents to find the best coalition to join. Previous work into QCGs has investigated the computational complexity of determining which is the best coalition to join. We plan to expand on this work by investigating the computational complexity of computing agent power in QCGs as well as by showing that insincere strategies, particularly bribery, are possible when the envy-freeness assumption is removed but that it is computationally difficult to identify the best agents to bribe. |
| Keywords: | Bribery, Coalition Formation, Computational Complexity |
| JEL: | C63 C78 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2007.100&r=gth |
| By: | Alexei Savvateev (New Economic School); Michel Le Breton (Universitè de Toulouse I, GREMAQ and IDEI); Valery Makarov (Central Economics and Mathematics Institute and New Economic School); Shlomo Weber (Southern Methodist University and CEPR) |
| Abstract: | We consider a model of the “world" with several regions that may create a unified entity or be partitioned into several unions (countries). The regions have distinct preferences over policies chosen in the country to which they belong and equally share the cost of public policies. It is known that stable \political maps" or country partitions, that do not admit a threat of secession by any group of regions, may fail to exist. To rectify this problem, in line with the recent trend for an increased autonomy and various regional arrangements, we consider federal structures, where a region can simultaneously be a part of several unions. We show that, under very general conditions, there always exists a stable federal structure. |
| Keywords: | Partitions, Federal Structures, Stability, Cooperative Games |
| JEL: | C71 D71 H41 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.41&r=gth |
| By: | Hans-Peter Weikard (Wageningen University); Rob Dellink (VU University Amsterdam) |
| Abstract: | This paper examines stability of international climate agreements for carbon abatement under an optimal transfer rule and renegotiations. The optimal transfer rule suggested to stabilise international environmental agreements (Weikard 2005, Carraro, Eyckmans and Finus 2006) is no longer optimal when agreements are renegotiated. We determine the conditions for optimal self-enforcing sequences of agreements. If these conditions are met, then transfer payments can be arranged such that no country wants to change its membership status at any stage. In order to demonstrate the applicability of our condition we use the STACO model, a 12-regions global model, to assess the impact of welldesigned transfer rules on the stability of an international climate agreement. Although there are strong free-rider incentives, we find a stable grand coalition in the first commitment period in a game with one round of renegotiations. |
| Keywords: | Stability of Coalitions, International Environmental Agreements, Partition Function Approach, Sharing Rules, Optimal Transfers, Renegotiations |
| JEL: | C72 D62 H41 H77 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2008.26&r=gth |
| By: | Andriy Zapechelnyuk; Ro'i Zultan |
| Abstract: | We consider a multitype population model with unobservable types, in which players are engaged in the `mutual help' game: each player can increase her partner's fitness at a cost to oneself. All individuals prefer free riding to cooperation, but some of them, helpers, can establish reciprocal cooperation in a long-term relationship. Such heterogeneity can drive cooperation through a partner selection mechanism under which helpers choose to interact with one another and shun non-helpers. However, in contrast to the existing literature, we assume that each individual is matched with an anonymous partner, and therefore, stable cooperation cannot be achieved by partner selection per se. We suggest that helpers can signal their type to one another in order to establish long-term relationships, and we show that a reliable signal always exists. Moreover, due to the difference in future benefits of a long-term relationship for helpers and non-helpers, the signal need not be a handicap, in the sense that the cost of the signal need not be correlated with type. |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp483&r=gth |