Matrix Games, Mixed Strategies, and Statistical Mechanics

Details Matrix Games, Mixed Strategies, and Statistical Mechanics Matrix Games, Mixed Strategies, and Statistical Mechanics

1998-09-20

arxiv.org/abs/cond-mat/9809265v1

Phys. Rev. Lett. 81, 4999-5002 (1998)

Physics

Condensed Matter

Disordered Systems and Neural Networks

submitted to PRL, for related information see http://itp.nat.uni-magdeburg.de/~jberg/games.html

Scientific paper

10.1103/PhysRevLett.81.4999

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results compared with numerical simulations.

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