- Question 3 30 Marks Two Players Odd And Even Each Secretively Think Of An Integer Between 1 And 3 Inclusive Both P 1 (25.17 KiB) Viewed 32 times
Question 3: (30 marks] Two players, Odd and Even, each secretively think of an integer between 1 and 3 inclusive. Both players reveal their numbers simultaneously. If the sum of the numbers is even, Even wins 3 dollars from Odd if the numbers are the same in which case the sum is obviously even). If the numbers are distinct, Even wins a number of dollars from Odd equal to the difference of the numbers. If the sum of the numbers is odd, then Odd wins a number of dollar from Even equal to the sum of the numbers. (a) Write down the payoff matrix for this game. (b) Are there pure strategies for Odd or Even which are dominated? (c) What are the optimal mixed strategies for Odd and Even? (d) Does this game favor any of the players?