The Mixed Strategy Algorithm

This lesson shows the algorithm we use to solve for mixed strategy Nash equilibrium in simple 2×2 games.

Takeaway Points

1. If there is a mixed strategy Nash equilibrium, it usually is not immediately obvious. (Do not let matching pennies lull you into believing this is easy!)
2. However, there is a straightforward algorithm that lets you calculate mixed strategy Nash equilibria. We will employ it frequently.
3. The algorithm involves setting the payoffs for a player’s two pure strategies equal to each other and solving for the mixed strategy of the other player that makes this equation true.
4. The mixed strategy algorithm does not involve any fancy mathematics. All one needs is basic knowledge of algebra. However, the process requires that the analyst be careful in putting the right values in the right places.
5. The trickiest part of the logic of mixed strategy Nash equilibrium is that we must use one player’s payoffs to solve for the player’s strategy. This is because the point of my mixed strategy is to make you indifferent, and vice versa.

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