Statistical Mechanics of Games

Statistical mechanics of spatial evolutionary games

We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash equilibria. We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their in...

Non-equilibrium statistical mechanics of Minority Games

In this paper I give a brief introduction to a family of simple but nontrivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disordered stochastic processes without detailed balance, the canonical technique f...

Statistical Mechanics of Two-player Iterated Games

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the deterministic policies with finite memory. In particular, we show that if one of the players has a generalized tit-for-tat policy, the mean payoff per move of both pla...

Statistical Mechanics

Statistical Mechanics

where pi ≡ p(x = i). If only M of the K states have non-zero probability and that probability is 1/M then S = logM . In this special case the entropy is the log of the number of occupied states. An analog of this special case in the continuous domain occurs in Liouville’s Theorem. This states that if the volume of phase space (i.e. of the x variable, but now multivariate and continuous) is some...