We consider population games played by procedurally rational players who, when revising their current strategy, test each of their available strategies independently in a series of random matches –i.e., a battery of tests–, and then choose the strategy that performed best in this battery of tests. This revision protocol leads to the so-called payoff-sampling dynamics (aka test-all Best Experienced Payoff dynamics).
In this paper we characterize the support of all the rest points of these dynamics in any game and analyze the asymptotic stability of the faces to which they belong. We do this by defining strategy sets closed under payoff sampling, and by proving that the identification of these sets can be made in terms of simple comparisons between some of the payoffs of the game.
