Reven and Coddy play a game in which they each simultaneously present a single hand with one or two fingers extended. Reven wins if the total number of fingers extended is even. Otherwise, Coddy wins. The loser pays the winner the number of dollars equal to the total number of fingers extended.
(a) What is the payoff matrix for the game?
(b) Determine the expected value of the game and the optimal strategies for Reven and Coddy?