Distribution of pure Nash equilibria in n-person games with random best replies
AbstractIn this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity.
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Bibliographic InfoPaper provided by Aboa Centre for Economics in its series Discussion Papers with number 71.
Date of creation: Dec 2011
Date of revision:
random games; pure Nash equilibria; n players;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-02 (All new papers)
- NEP-GTH-2012-05-02 (Game Theory)
- NEP-HPE-2012-05-02 (History & Philosophy of Economics)
- NEP-MIC-2012-05-02 (Microeconomics)
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