Consider a game where two players, A and B, bet 1, 2 or 3. If the bets are equal then no one wins, if the product of the bets is even the player with the smaller bet wins otherwise the larger bet wins. Thus, if A plays 1 and B plays 2 then A wins 2.

i. What is the payoff matrix for this game?

ii. Find the optimal strategy for each player.

(b) Consider a matrix game with two players A and B. Player A has 2 possible strategies and player B has 4 possible strategies.

The payoff matrix for this game is given by

2	-1	0	2
-1	1	2	1

. i. Show that no saddle point solution exists.

ii. Determine the optimal mixed strategy solution for A.

iii. Use the result in ii. to determine the optimal mixed strategy for B and find the corresponding average payoff.