Evolution and Equilibria Selection of Repeated Lattice Games

In this paper we study the configuration dynamics and the societal equilibrium selection of repeated lattice games. Each player plays games only with his immediate neighbors hence indirectly interacts with everyone else. A player may or may not have perfect control over his action. Different updating orderings at the society level are adopted and compared. The following conclusions are reached. (i) Under best-response dynamics the society locks in with probability one to a pure-strategy Nash configuration for the class of (weakly) acyclic lattice games when players do not move simultaneously. (ii) Under limited control, the configuration dynamics is ergodic with a unique invariant distribution having an explicit Gibbs representation. (iii) By allowing imperfect control over action to become perfect the Pareto Dominant Nash configurations will be selected stochastically.