Assume a game with two players, A and B, who raise one or both hands concurrently. A wins if total number of hands raised is odd, and B wins in other way. The amount won refers to the total number of hands raised, and is paid by loser to the winner.

a) Write down the matrix form of the game. Is there a pure strategy solution? Explain your answer.

b) Assume B raises one hand half of time and two hands the other half of the time. Explain 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? Specify the expected payoff for A if A raises one hand 75% of time and two hands 25% of the time?