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Log-linear Dynamics and Local Potential

By Daijiro Okada and Olivier Tercieux

Abstract

We show that local potential maximizer (\cite{morris+05}) with constant weights is stochastically stable in the log-linear dynamics provided that the payoff function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of our main results as well as other concepts closely related to local potential maximizer: weighted potential maximizer, p-dominance. We also discuss the log-linear processes where each player's stochastic choice rule converges to the best response rule at different rates. For 2 player 2 action games, we examine a modified log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically stable. This in particular implies that for 2 player 2 action games a strict (p1,p2)-dominant equilibrium with p1+p2Log-linear dynamics, Stochastic stability, Local potential maximizer, Equilibrium selection, Comparison of Markov Chains

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