Quantitative Analysis for Management, 13/e

M4.3 Pure Strategy Games

When a saddle point is present, the strategy each player should follow will always be the same, regardless of the other player’s strategy. This is called a pure strategy. A saddle point is a situation in which both players are facing pure strategies.

A pure strategy exists whenever a saddle point is present.

Using the minimax criterion, we saw that the game in Table M4.2 had a saddle point and thus is an example of a pure strategy game. It is beneficial for player X and for player Y to always choose one strategy. Simple logic would lead us to this same conclusion. Player X will always select $X_1$, since the payoffs for $X_1$ are better than the payoffs for $X_2,$ regardless of what player Y does. Knowing that player X will ...