Consider a three-player game where player 1 can choose strategy A or strategy B, player 2 can choose strategy C or strategy D, and player 3 can choose strategy E or strategy F. The payoff matrix is given as follows:

	C	D
A E	1,2,3	4,5,6
A F	7,8,9	10,11,12
B E	13,14,15	16,17,18
B F	19,20,21	22,23,24

(a) Write down the pure strategy Nash equilibrium of the game, if it exists.

(b) Suppose player 1 and player 2 are coordinating and want to guarantee a joint payoff of at least 15. What strategy combination should they choose, and what is the maximum payoff that player 3 can receive?

(c) Find the expected payoff for each player if they all choose a mixed strategy that gives each available strategy an equal probability of being played.

Show all calculations and give your answer in full details.

Answer rating: 100% (QA)

The detailed answer for the above question is provided below a To find the pure strategy Nash equilibrium of the game we need to find a strategy combi... View the full answer