Log-linear Dynamics and Local Potential

We show that local potential maximizer ([15]) with constant weights is stochas- tically stable in the log-linear dynamics provided that the payo® 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 di®erent rates. For 2£2 games, we examine a modi¯ed log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically sta- ble. This in particular implies that for 2 £ 2 games a strict (p1; p2)-dominant equilibrium with p1 + p2 < 1 is stochastically stable under the new dynamics.