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...

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) (5 pts) Write down the matrix form of the game. Is there a pure strategy solution?
Explain your answer.
(b) (10 pts) 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?