The Statistical Mechanics of Strategic Interaction

TLDR

Players on a lattice interact only with a finite set of neighbors, yet any two players are indirectly connected via finite chains of direct interactions. The study investigates strategic interaction among lattice-based players. The authors analyze stochastic strategy revision processes—such as myopic best response and stochastic choice—examining their stationary distributions and long‑run Markov dynamics. Stationary distributions are partially characterized, and for nearly best‑response stochastic choice processes, asymptotic behavior links to equilibrium selection in symmetric coordination games. JEL classification: C78.

Abstract

I study strategic interaction among players who live on a lattice. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite chain of direct interactions. I examine various stochastic strategy revision processes, including (myopic) best response and stochastic choice. I discuss both stationary distributions and the limit behavior of these Markov processes. Stationary distributions are partially characterized, and the asymptotic behavior of stochastic choice for those processes whose choice rule is nearly best-response is related to equilibrium selection in symmetric 2 × 2 and n × n coordination games. Journal of Economic Literature Classification Number: C78.