This lesson uses matching pennies to introduce the concept of mixed strategy Nash equilibrium.
- If the game is finite and there are no pure strategy Nash equilibrium, then there must be a mixed strategy Nash equilibrium.
- In a mixed strategy Nash equilibrium, at least one of the players plays multiple strategies with positive probability.
- This mixed strategy leaves the opponent indifferent to playing his pure strategies. (When there are more than two strategies, this gets a little more complicated—it may be the mixed strategy leaves the other player indifferent between playing two of his strategies and strictly worse off playing a third.)