Local interactions and p-best response set

We study a local interaction model where agents play a finite n-person game following a perturbed best-response process with inertia. We consider the concept of minimal p-best response set to analyze distributions of actions in the long run. We distinguish between two assumptions made by agents about the matching rule. We show that only actions contained in the minimal p-best response set can be selected provided p is sufficiently small. We demonstrate that these predictions are sensitive to the assumptions about the matching rule.