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Evolving mixed nash equilibria for bimatrix games

Published: 07 July 2012 Publication History

Abstract

In a mixed strategy equilibrium players randomize between their actions according to a very specific probability distribution, even though with regard to the game payoff, they are indifferent between their actions. Currently, there is no compelling model explaining why and how agents may randomize their decisions is such a way, in real world scenarios. In this paper we experiment with a model for bimatrix games, where the goal of the players is to find robust strategies for which the uncertainty in the outcome of the opponent is reduced as much as possible. We show that in an evolutionary setting, the proposed model converges to mixed strategy profiles, if these exist. The result suggest that only local knowledge of the game is sufficient to attain the adaptive convergence.

References

[1]
R.J. Aumann. What is game theory trying to accomplish? In Frontiers of Economics, edited by K. Arrow and S. Honkapohja. Citeseer, 1985.
[2]
Kalyanmoy Deb et al. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimisation: NSGA-II. In Marc Schoenauer et al., editor, PPSN VI, volume 1917 of LNCS, pages 849--858, Paris, France, 16--20 Sept 2000. Springer-Verlag.
[3]
J.C. Harsanyi. Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points. International Journal of Game Theory, 2(1):1--23, 1973.

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cover image ACM Conferences
GECCO '12: Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
July 2012
1586 pages
ISBN:9781450311786
DOI:10.1145/2330784

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 July 2012

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  1. mixed nash

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GECCO '12
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GECCO '12: Genetic and Evolutionary Computation Conference
July 7 - 11, 2012
Pennsylvania, Philadelphia, USA

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