We study repeated interactions among a fixed set of “low rationality” players who have status
quo actions, randomly sample other actions, and change their status quo if the sampled
action yields a higher payoff. This behavior generates a random process, the better-reply
dynamics. Long run behavior leads to Nash equilibrium in games with the weak finite
improvement property, including finite, supermodular games and generic, continuous, two-
player, quasi-concave games. If players make mistakes and if several players can sample at …