Consider a game with two players, A and B, who raise one or both hands simultaneously. A wins if the total number of hands raised is odd, and B wins otherwise. The amount won is the total number of hands raised, and is paid by the loser to the winner.
(a) prepare down the matrix form of the game. Is there a pure strategy solution?
describe your answer.
(b)  Suppose B raises one hand half of the time and two hands the other half of the time. What is the expected payoff for A if A also raises one hand half of the time and two hands the other half of the time? What is the expected payoff for A if A raises one hand 75% of the time and two hands 25% of the time?