Consider the following two-player game. Players one and two simultaneously and independently choose integers weakly between -30 and 30, x1 and x2 ? {-30, -29, -28, . . ., 30}. Player one's payoff is 100 if she chooses the square of the other player's integer. Player two's payoff is 100 if he chooses the cube root of player one's integer. Otherwise each player's payoff is equal to 69 minus his or her choice.