Consider a game in which player 1 first selects between I and O. If player 1 selects O, then the game ends with the payoff vector (x, 1) (x for player 1), where x is some positive number. If player 1 selects I, then this selection is revealed to player 2 and then the players play the battle-of-the-sexes game in which they simultaneously and independently choose between A and B. If they coordinate on A, then the payoff vector is (3, 1). If they coordinate on B, then the