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To check for mixed strategy Nash equilibria, we must run the mixed strategy algorithm. This algorithm shows whether there exists a mixed strategy for a player that leaves the other player indifferent between his or her two pure strategies. If such a mixed strategy exists for both players, then those strategies collectively form a mixed strategy Nash equilibrium.

The mixed strategy algorithm is the first computationally intensive part of game theory we have encountered. However, we will be using the algorithm quite a bit later on, so do not be worried if the logic of the math is difficult to grasp at first.