This lesson shows how to calculate payoffs for mixed strategy Nash equilibria.
To calculate payoffs in mixed strategy Nash equilibria, do the following:
- Solve for the mixed strategy Nash equilibrium. Write the probabilities of playing each strategy next to those strategies.
- For each cell, multiply the probability player 1 plays his corresponding strategy by the probability player 2 plays her corresponding strategy. Write this in the cell.
- Choose which player whose payoff you want to calculate. Multiply each probability in each cell by his or her payoff in that cell.
- Sum these numbers together. This is the expected payoff in the mixed strategy Nash equilibrium for that player.