Fictitious play in coordination games'

We study the Fictitious Play process with bounded and unbounded recall in p ure coordination games for which failing to coordinate yields a payoff of z ero for both players. It is shown that every Fictitious Play player with bo unded recall may fail to coordinate against his own type. On the other hand , players with unbounded recall are shown to coordinate (almost surely) aga inst their own type as well as against players with bounded recall. In part icular, this implies that a FP player's realized average utility is (almost surely) at least as large as his minmax payoff in 2 x 2 coordination games .