Solved Problem M4-1
George Massic (player X) faces the following game. Using dominance, reduce the size of the game, if possible.
Y1
Y2
X1
6
5
X2
20
23
X3
15
11
Solution
After carefully analyzing the game, George realizes that he will never play strategy X1. The best outcome for this strategy (6) is worse than the worst outcome for the other two strategies. In addition, George would never play strategy X3, for the same reason. Thus, George will always play strategy X2. Given this situation, player Y would always play strategy Y1 to minimize her losses. This is a pure strategy game with George playing X2 and person Y playing strategy Y1. The value of the game for this problem is the outcome of these two strategies, which is 20.
Solved Problem M4-2 Using the solution procedure for a mixed strategy game, solve the following game:
Y1
Y2
X1
4
2
X2
0
10
Solution
This game can be solved by setting up the mixed strategy table and developing the appropriate equations: