Josef Hofbauer and Karl Schlag (1998):
Sophisticated Imitation in Cyclic Games
(Revised Version, August 2000).
Published in J. Evolutionary Economics 10 (2000), 523-543.
Individuals belonging to two large populations are repeatedly randomly
matched to play a cyclic 2x2 game such as Matching Pennies. Between
matching rounds, individuals sometimes change their strategy after observing
a finite sample of other outcomes within their population. Individuals from
the same population follow the same behavioral rule.
In the resulting discrete time dynamics the unique Nash equilibrium is unstable.
However, for sample sizes greater than one, we present an
imitation rule where long run play cycles closely around the equilibrium.
preprint ( dvi ), or reprint.