  We characterize the class of symmetric two-player games in which tit-for-tat
cannot be beaten even by very sophisticated opponents in a repeated game. It
turns out to be the class of exact potential games. More generally, there is a
class of simple imitation rules that includes tit-for-tat but also
imitate-the-best and imitate-if-better. Every decision rule in this class is
essentially unbeatable in exact potential games. Our results apply to many
interesting games including all symmetric 2x2 games, and standard examples of
Cournot duopoly, price competition, public goods games, common pool resource
games, and minimum effort coordination games.
