Quantitative Analysis for Management, 13/e

M4.4 Mixed Strategy Games

When there is no saddle point, players will play each strategy for a certain percentage of the time. This is called a mixed strategy game. The most common way to solve a mixed strategy game is to use the expected gain or loss approach. The goal of this approach is for a player to play each strategy a particular percentage of the time so that the expected value of the game does not depend on what the opponent does. This will occur only if the expected value of each strategy is the same.

In a mixed strategy game, each player should optimize the expected gain.

Consider the game shown in Table M4.4. There is no saddle point, so this will be a mixed strategy game. Player Y must determine the percentage of the time to play ...