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on Game Theory |
| By: | Ciftci,Baris; Dimitrov,Dinko (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we study hedonic coalition formation games in which players' preferences over coalitions are induced by a semi-value of a monotonic simple game with veto control. We consider partitions of the player set in which the winning coalition contains the union of all minimal winning coalitions, and show that each of these partitions belongs to the strict core of the hedonic game. Exactly such coalition structures constitute the strict core when the simple game is symmetric. Provided that the veto player set is not a winning coalition in a symmetric simple game, then the partition containing the grand coalition is the unique strictly core stable coalition structure. |
| Keywords: | Banzhaf value;hedonic game;semi-value;Shapley value;simple game;strict core |
| JEL: | D72 C71 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2006114&r=gth |
| By: | Ciftci,Baris; Borm,Peter; Hamers,Herbert (Tilburg University, Center for Economic Research) |
| Abstract: | A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player's payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. We show that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. Extensions of these results to other probabilistic values are discussed. |
| Keywords: | cooperative games;simple games;population monotonic path schemes;coalition formation;probabilistic values |
| JEL: | C71 D72 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2006113&r=gth |
| By: | Christophe Labreuche (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - [CNRS : UMR137][THALES]); Michel Grabisch (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]) |
| Abstract: | Bi-cooperative games have been introduced by Bilbao as a generalization of classical cooperative games, where each player can participate positively to the game (defender), negatively (defeater), or do not participate (abstentionist). In a voting situation (simple games), they coincide with ternary voting game of Felsenthal and Mochover, where each voter can vote in favor, against or abstain. In this paper, we propose a definition of value or solution concept for bi-cooperative games, close to the Shapley value, and we give an interpretation of this value in the framework of (ternary) simple games, in the spirit of Shapley-Shubik, using the notion of swing. Lastly, we compare our definition with the one of Felsenthal and Machover, based on the notion of ternary roll-call, and the Shapley value of multi-choice games proposed by Hsiao and Ragahavan. |
| Keywords: | Cooperative game theory, bi-cooperative games, power index, Shapley value. |
| Date: | 2006–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00113340_v1&r=gth |
| By: | Björnerstedt, Jonas (Swedish Competition Authority); Westermark, Andreas (Department of Economics) |
| Abstract: | This paper studies infinite-horizon bargaining between a seller and multiple buyers when externalities are present. We extend the analysis in Jehiel & Moldovanu (1995a), by allowing for both pure and mixed equilibria. This extension is warranted, since under some circumstances,the complexity of the equilibria with bounded recall they analyze tend to infinity as players become very patient. We show that stationary subgame perfect equilibria always exist. Moreover, a characterization of the stationary subgame perfect equilibria in generic games is presented. Equilibria with delay exist only for strong positive externalities. Since ach buyer receives a positive payoff when the seller agrees with some other buyer, positive externalities induces a war of attrition between buyers. Furthermore, the results when analyzing mixed stationary equilibria are different than when focusing on pure strategies with bounded recall as Jehiel & Moldovanu (1995a). Specifically, they find delay only when externalities are negative. |
| Keywords: | Bargaining; externalities; delay |
| JEL: | C72 C78 D62 |
| Date: | 2006–11–24 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:uunewp:2006_029&r=gth |
| By: | Pradeep Dubey (Center for Game Theory in Economics, Stony Brook); Rahul Garg (IBM India Research Lab, New Delhi) |
| Abstract: | We consider a communications network in which users transmit beneficial information to each other at a cost. We pinpoint conditions under which the induced cooperative game is supermodular (convex). Our analysis is in a lattice-theoretic framework, which is at once simple and able to encompass a wide variety of seemingly disparate models. |
| Keywords: | Information lattice, Multicast/unicast transmission, Cooperative games, Shapley value, Convex/supermodular games |
| JEL: | C71 D82 L96 |
| Date: | 2006–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1592&r=gth |
| By: | Caprari,E.; Patrone,F.; Pusillo,L.; Tijs,S.; Torre,A. (Tilburg University, Center for Economic Research) |
| Abstract: | In many share problems there is a priori given a natural set of possible divisions to solve the sharing problem. Cooperative games related to such share sets are introduced, which may be helpful in solving share problems. Relations between properties of share sets and properties of games are investigated. The average lexicographic value for share sets and for cooperative games is studied. |
| Keywords: | cooperative games;bankruptcy games;average lexicographic value;opportunity sets |
| JEL: | C71 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2006115&r=gth |
| By: | Engwerda,Jacob (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games. We will review the open-loop and feedback information case. In both cases we address both the finite and the infinite-planning horizon. |
| Keywords: | Algebraic Riccati equations;linear quadratic differential games;Nash equilibria |
| JEL: | C61 C72 C73 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2006109&r=gth |
| By: | Engwerda,Jacob (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we review some basic results on linear quadratic differential games. We consider both the cooperative and non-cooperative case. For the non-cooperative game we consider the open-loop and (linear) feedback information structure. Furthermore the effect of adding uncertainty is considered. The overview is based on [9]. Readers interested in detailed proofs and additional results are referred to this book. |
| Keywords: | linear-quadratic games;Nash equilibrium;affine systems;solvability conditions;Riccati equations |
| JEL: | C61 C72 C73 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2006110&r=gth |
| By: | Engwerda,Jacob (Tilburg University, Center for Economic Research) |
| Abstract: | In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson [15], this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strong d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic. |
| Keywords: | Nash bargaining solution;d-monotonicity;diagonally dominant Stieltjes matrix |
| JEL: | C61 C62 C71 C78 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2006107&r=gth |
| By: | Lu, Jingfeng |
| Abstract: | This paper studies endogenous entry and ex ante revenue-maximizing auctions in an independent private value setting where potential bidders have private-information entry costs. The contribution of this paper is four-fold. First, we show that any equilibrium entry can be characterized through a set of continuous and monotonic shutdown curves that separate the bidders' types into participating and nonparticipating categories. Second, the expected winning probability of a participant does not depend on his private entry cost. Furthermore, the expected winning probabilities of the participating types are given by the slopes of the shutdown curves. Third, symmetric entry equilibria (shutdown curves) implemented by the classes of ex post efficient or ex post revenue-maximizing mechanisms are completely characterized. Fourth, within these two classes of mechanisms, a modified Vickrey auction with uniform reserve price and entry subsidy is ex ante revenue-maximizing. The desired entry subsidy and reserve price are determined by the lower end of the corresponding shutdown curve. |
| Keywords: | Auctions Design; Ex Post Efficiency; Endogenous Participation; Multidimensional Screening; Vickrey Auction. |
| JEL: | D44 D82 |
| Date: | 2006–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:934&r=gth |
| By: | CESI BERARDINO |
| Abstract: | It is shown that, in a dynamic competition, an exogenous horizontal merger is profitable even if a small share of active firms merge. However, each firm has incentive to remain outside the merger because it would benefit more (Insiders' dilemma). We show that in an infinite repeated game in which the firms use trigger strategies an exogenous bilateral merger can be profitable and the Insiders' dilemma is mitigated. |
| Date: | 2006–03 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceiswp:229&r=gth |
| By: | Staffiero, Gianandrea (IESE Business School) |
| Abstract: | Wide experimental evidence shows that people do care about their opponents' payoff during social interaction. Our research aims to shed light on the relative importance of different motives in non-selfish choices highlighted in the recent literature. After a standard public-good game, one player is given the possibility to increase or decrease his opponent's payoff. While our baseline treatment replicates the tendency to hurt richer but lower-contributing players and help poorer but higher-contributing players, if we add exogenous assignments we find substantial willingness to hurt the rich, even if they have contributed more, and to help the poor, even if they have contributed less. These results show a greater focus on correcting inequality than on punishing or rewarding particular behavior. Moreover, we also find that subjects disregard efficiency, in terms of the overall "pie" to be shared. Overall, our data support inequality aversion as a more robust phenomenon than reciprocity and efficiency considerations. |
| Keywords: | Fairness; Cooperation; Inequality; Reciprocity; |
| JEL: | C91 D63 H41 |
| Date: | 2006–09–24 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:iesewp:d-0652&r=gth |