Player A and B each announce a color (red, white, blue, or green) simultaneously. The winner is determined by the following rules: red beats white, white beats blue, blue beats green, and green beats red. If both players announce the same color the game is a draw. The payoffs work as follows, if player A wins with red, she wins 5, if player A wins with white or blue, she wins 2, and if player A wins with green, she wins 3. If player B wins with red or white, he wins 4, if player B wins with blue he wins 3, and if player B wins with green he wins 5. The above description leaves out the cases where players announce colors that are not directly comparable. For example, there is no rule for what happens if one player announces white and the other announces green. In these situations, the winner is determined by examining the number of letters in each color that is announced. If both colors have the same number of letters, then the game is a draw. If there are a different number of letters in the announced colors, then the player who announced the color with the fewest letters wins an amount equal to the sum of the number of letters in both of the announced colors. A. What is the value of this game and what are the optimal strategies for each player? Which player wins? B. Suppose that there is one change to the payoff rules: “if player A wins with white or blue, she wins 4”. What is the value of this game and what are the optimal strategies for each player? Which player wins?
Player A and B each announce a color (red, white, blue, or green) simultaneously. The winner is determined by the following rules: red beats white, white beats blue, blue beats green, and green beats red. If both players announce the same color the game is a draw. The payoffs work as follows, if player A wins with red, she wins 5, if player A wins with white or blue, she wins 2, and if player A wins with green, she wins 3. If player B wins with red or white, he wins 4, if player B wins with blue he wins 3, and if player B wins with green he wins 5. The above description leaves out the cases where players announce colors that are not directly comparable. For example, there is no rule for what happens if one player announces white and the other announces green. In these situations, the winner is determined by examining the number of letters in each color that is announced. If both colors have the same number of letters, then the game is a draw. If there are a different number of letters in the announced colors, then the player who announced the color with the fewest letters wins an amount equal to the sum of the number of letters in both of the announced colors.
A. What is the value of this game and what are the optimal strategies for each player? Which player wins?
B. Suppose that there is one change to the payoff rules: “if player A wins with white or blue, she wins 4”. What is the value of this game and what are the optimal strategies for each player? Which player wins?
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