We consider sampling best response decision protocols with statistical inference
in population games. Under these protocols, a revising agent observes the actions of
k randomly sampled players in a population, estimates from the sample a probability distribution for the state of the population (using some inference method), and
chooses a best response to the estimated distribution. We formulate deterministic
approximation dynamics for these protocols. If the inference method is unbiased,
strict Nash equilibria are rest points, but they may not be stable. We present tests for
stability of pure equilibria under these dynamics. Focusing on maximum-likelihood
estimation, we can define an index that measures the strength of each strict Nash
equilibrium. In tacit coordination or weakest-link games, the stability of equilibria
under sampling best response dynamics is consistent with experimental evidence,
capturing the effect of strategic uncertainty and its sensitivity to the number of players and to the cost/benefit ratio.
