The Experts below are selected from a list of 72918 Experts worldwide ranked by ideXlab platform
Licun Xue - One of the best experts on this subject based on the ideXlab platform.
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Negotiation-proof Nash Equilibrium
Social Science Research Network, 2001Co-Authors: Licun XueAbstract:This paper defines "negotiation-proof Nash Equilibrium", a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections; moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof Nash Equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of coalition-proof Nash Equilibrium. (2) The negotiation process is formalized by a "graph", which serves as a natural extension to the approach that models preplay communication by an extensive game. Key words: coalition, negotiation, Nash Equilibrium, self-enforcing agreement, perfect foresight
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Negotiation-proof Nash Equilibrium
International Journal of Game Theory, 2000Co-Authors: Licun XueAbstract:This paper defines “negotiation-proof Nash Equilibrium'', a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections; moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof Nash Equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of coalition-proof Nash Equilibrium. (2) The negotiation process is formalized by a “graph”, which serves as a natural extension to the approach that models preplay communication by an extensive game.
Ludovic Renou - One of the best experts on this subject based on the ideXlab platform.
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Implementation in mixed Nash Equilibrium
Journal of Economic Theory, 2012Co-Authors: Claudio Mezzetti, Ludovic RenouAbstract:A mechanism implements a social choice correspondence f in mixed Nash Equilibrium if at any preference profile, the set of all pure and mixed Nash Equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash Equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash Equilibrium.
Aviad Rubinstein - One of the best experts on this subject based on the ideXlab platform.
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Communication complexity of Nash Equilibrium in potential games.
arXiv: Computer Science and Game Theory, 2020Co-Authors: Yakov Babichenko, Aviad RubinsteinAbstract:We prove communication complexity lower bounds for (possibly mixed) Nash Equilibrium in potential games. In particular, we show that finding a Nash Equilibrium requires $poly(N)$ communication in two-player $N \times N$ potential games, and $2^{poly(n)}$ communication in $n$-player two-action games. To the best of our knowledge, these are the first results to demonstrate hardness in any model of (possibly mixed) Nash Equilibrium in potential games.
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Inapproximability of Nash Equilibrium
SIAM Journal on Computing, 2018Co-Authors: Aviad RubinsteinAbstract:We prove that finding an $\epsilon$-approximate Nash Equilibrium is $\mathsf{PPAD}$--complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As corollaries, we also prove similar inapproximability results for Bayesian Nash Equilibrium in a two-player incomplete information game with a constant number of actions, for relative $\epsilon$-well supported Nash Equilibrium in a two-player game, for market Equilibrium in a nonmonotone market, for the generalized circuit problem defined by Chen, Deng, and Teng [J. ACM, 56 (2009)], and for approximate competitive Equilibrium from equal incomes with indivisible goods.
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inapproximability of Nash Equilibrium
Symposium on the Theory of Computing, 2015Co-Authors: Aviad RubinsteinAbstract:We prove that finding an e-approximate Nash Equilibrium is PPAD-complete for constant e and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As corollaries, we also prove similar inapproximability results for Bayesian Nash Equilibrium in a two-player incomplete information game with a constant number of actions, for relative e-Nash Equilibrium in a two-player game, for market Equilibrium in a non-monotone market, for the generalized circuit problem defined by Chen et al. [4], and for approximate competitive Equilibrium from equal incomes with indivisible goods.
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STOC - Inapproximability of Nash Equilibrium
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing, 2015Co-Authors: Aviad RubinsteinAbstract:We prove that finding an e-approximate Nash Equilibrium is PPAD-complete for constant e and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As corollaries, we also prove similar inapproximability results for Bayesian Nash Equilibrium in a two-player incomplete information game with a constant number of actions, for relative e-Nash Equilibrium in a two-player game, for market Equilibrium in a non-monotone market, for the generalized circuit problem defined by Chen et al. [4], and for approximate competitive Equilibrium from equal incomes with indivisible goods.
Christos H Papadimitriou - One of the best experts on this subject based on the ideXlab platform.
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The complexity of computing a Nash Equilibrium
Communications of the ACM, 2009Co-Authors: Constantinos Daskalakis, Paul W Goldberg, Christos H PapadimitriouAbstract:How long does it take until economic agents converge to an Equilibrium? By studying the complexity of the problem of computing a mixed Nash Equilibrium in a game, we provide evidence that there are games in which convergence to such an Equilibrium takes prohibitively long. Traditionally, computational problems fall into two classes: those that have a polynomial-time algorithm and those that are NP-hard. However, the concept of NP-hardness cannot be applied to the rare problems where "every instance has a solution"---for example, in the case of games Nash's theorem asserts that every game has a mixed Equilibrium (now known as the Nash Equilibrium, in honor of that result). We show that finding a Nash Equilibrium is complete for a class of problems called PPAD, containing several other known hard problems; all problems in PPAD share the same style of proof that every instance has a solution.
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the complexity of computing a Nash Equilibrium
Symposium on the Theory of Computing, 2006Co-Authors: Constantinos Daskalakis, Paul W Goldberg, Christos H PapadimitriouAbstract:We resolve the question of the complexity of Nash Equilibrium by showing that the problem of computing a Nash Equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomial time solvability of normal form games and graphical games, establishing that these kinds of games can simulate a PPAD-complete class of Brouwer functions.
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STOC - The complexity of computing a Nash Equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06, 2006Co-Authors: Constantinos Daskalakis, Paul W Goldberg, Christos H PapadimitriouAbstract:We resolve the question of the complexity of Nash Equilibrium by showing that the problem of computing a Nash Equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomial time solvability of normal form games and graphical games, establishing that these kinds of games can simulate a PPAD-complete class of Brouwer functions.
Arnaud Legrand - One of the best experts on this subject based on the ideXlab platform.
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Nash Equilibrium based fairness
Mathematical Methods of Operations Research, 2012Co-Authors: Hisao Kameda, Eitan Altman, Corinne Touati, Arnaud LegrandAbstract:There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash Equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash Equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash Equilibrium. We consider this Pareto optimum to be ‘Nash Equilibrium based fair.’ We further define a ‘Nash proportionately fair’ Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash Equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations.
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Nash Equilibrium based fairness
Mathematical Methods of Operations Research, 2012Co-Authors: Hisao Kameda, Eitan Altman, Corinne Touati, Arnaud LegrandAbstract:International audienceThere are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash Equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash Equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash Equilibrium.We consider this Pareto optimum to be 'Nash Equilibrium based fair.'We further define a 'Nash proportionately fair' Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash Equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations
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GAMENETS - Nash Equilibrium based fairness
2009Co-Authors: Hisao Kameda, Eitan Altman, Corinne Touati, Arnaud LegrandAbstract:There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash Equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash Equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash Equilibrium. We consider this Pareto optimum to be “Nash Equilibrium based fair.” We further define a “Nash proportionately fair” Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash Equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations.
