A two-person, zero-sum game is played as follows. Player 1 is given the aces of spades and diamonds, and the two of hearts. Player 2 is given the aces of hearts and clubs, and the two of spades. Each then chooses a card, and there are shown simultaneously, with payoffs as follows. If both cards are of the same suit, then the ace beats the two. If the cards are of different suits and different denominations, then the black card beats the red. If they are of the same denominations, then the red card beats the black. If they are both black aces or both red aces, there is a standoff. In any case, the player winning will win as many dollars as there are spots on his opponent's card.
(a) Write the payoff matrix for player 1.
(b) Find the optimal strategies for the players according to the minimax criterion and find the value of the game.
(a) Write the payoff matrix for player 1.
(b) Find the optimal strategies for the players according to the minimax criterion and find the value of the game.