Suppose that the player who chooses the larger number wins. If the row player chooses the larger number, she wins the sum of the two numbers from the column player. If the column player wins, he wins the difference of the two numbers from the row players. If each player chooses the same number the game is a draw. What are the optimal strategies for each player, and what is the value of the game?
Next, suppose that we have a different set of payoffs. If the sum of the numbers is odd, then row player wins the sum of the numbers from the column player. If the sum of the numbers is even, then the column player wins the sum of the numbers from the row player. What are the optimal strategies for each player, and what is the value of the game?