We study a family of population game dynamics under which each revising agent
randomly selects a set of strategies according to a given test-set rule; tests each strategy
in this set a fixed number of times, with each play of each strategy being against a
newly drawn opponent; and chooses the strategy whose total payoff was highest,
breaking ties according to a given tie-breaking rule. These dynamics need not respect
dominance and related properties except as the number of trials become large. Strict
Nash equilibria are rest points but need not be stable. We provide a variety of sufficient
conditions for stability and for instability, and illustrate their use through a range of
applications from the literature.
