. Consider the game below, and assume throughout this question that players can

Question

. Consider the game below, and assume throughout this question that players can only use pure strategies a. What is player I's (pure) maxmin strategy? b. What is player 2's (pure) maxmin strategy? c. What (pure) strategy should player I use to minmax player 2? d. What (pure) strategy should player 2 use to minmax player 1? e. The minmax theorem asserts that minmax and maxmin payoffs should be equivalent, which appears not to be the case here. Why does the minmax theorem not apply to this example? A 2.43,2 B 4,1 2.3 | 5,3 | 0,4 D 1.2 1.2 E 44 3.3

Explanation / Answer

Minimum payoff that player 1 may get is when B choose L is 1 and when it chooses R is 0. So, the maximum of these minimum payoffs is 1. So player 1’s maxmin strategy is D.

For player 2 minimum payoff he can get when 1 chooses A is 2, with 1 choosing B is 1, with 1 choosing C is 3, with 1 choosing D is 2, with 1 choosing E is 3. The maximum of these payoff is 3. So the maxmin strategy is {L,R}.

For player 2 maximum payoff he can get when player 1 chooses A is 4, with player 1 choosing B is 3, with player 1 choosing C is 4, with player 1 choosing D is 2, with player 1 choosing E is 4. The minimum of these payoff is 3. So player 1 should use D to minmax player 2.

Maximum payoff that player 1 may get is when B choose L is 5 and when it chooses R is 3. So, the minimum of these maximum payoffs is 3. So player 2 should use R to minmax player 1.

*WE are supposed to do four sub-parts . For answers to other pats post as a different question.

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