Sophisticated imitation in cyclic games

Individuals belonging to two large populations are repeatedly randomly matc hed to play a cyclic 2 x 2 game such as Matching Pennies. Between matching rounds, individuals sometimes change their strategy after observing a finit e sample of other outcomes within their population. Individuals from the sa me population follow the same behavioral rule. In the resulting discrete ti me dynamics the unique Nash equilibrium is unstable. However, for sample si zes greater than one, we present an imitation rule where long run play cycl es closely around the equilibrium.