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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.
Lawrence E. Blume (Thu,) studied this question.