1998/09/20 by Johannes Berg, J. Berg, A. Engel +1
Decision Sciences · Physics and Astronomy · Social Sciences · #Evolutionary Game Theory and Cooperation #Game Theory and Applications #Opinion Dynamics and Social Influence #adap-org #cond-mat.dis-nn #nlin.AO
paper · pdf · doi:10.1103/physrevlett.81.4999
published as Phys. Rev. Lett. 81, 4999-5002 (1998) · submitted to PRL, for related information see http://itp.nat.uni-magdeburg.de/~jberg/games.html
arxiv created 1998/09/20 · openalex publication_date 1998/11/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 are compared with numerical simulations.