This document describes a two-person zero-sum game between two players, Player A and Player B, who each have three strategy options. The payoff table shows the gains for Player A based on the strategies chosen. There is no optimal pure strategy for either player. However, the mixed strategy probabilities can be found algebraically, resulting in a value of 3 for the game.

1. Consider the following two-person zero-sum game. Assume the two players have the same three
strategy options. The payoff table below shows the gains for Player A.
Player B
Player A
Strategy b1
Strategy b2
Strategy b3
Strategy a1
5
6
-1
Strategy a2
1
1
2
Strategy a3
4
5
3
a. Is there an optimal pure strategy for this game? If so, what is it?
b. If not, can the mixed-strategy probabilities be found algebraically? What is the value of the
game?
Player B
Player A
Strategy b1

2. Strategy b2
Strategy b3
Strategy a1
5
6
-1
Strategy a2
1
1
2
Strategy a3
4
5
3