Perfect information games where each player acts only once

We study perfect information games played by an infinite sequence of players, each acting only once in the course of the game. We introduce a class of frequency-based minority games and show that these games have no subgame perfect $$\epsilon $$ ϵ -equilibrium for any $$\epsilon $$ ϵ sufficiently small. Furthermore, we present a number of sufficient conditions to guarantee existence of subgame perfect $$\epsilon $$ ϵ -equilibrium.