The mixed strategy Nash equilibrium is one of the most fundamental concepts within game theory and solving it can yield significant insights into how to behave in strategic behaviors. In this video, we learn how to solve for the mixed strategy Nash equilibrium using an example from a baseball game with a pitcher and a hitter.
Here is the payoff matrix:
The hitter can plan for a fastball or plan for a curveball, and the pitcher can throw a fastball or curveball. Naturally, the hitter would like to plan for the right pitch, whereas the pitcher would like to throw the pitch the hitter isn’t anticipating. There is no pure strategy Nash equilibrium, because at each outcome, one of the players would like to switch their choice. So the mixed strategy Nash equilibrium involves playing each strategy some percentage of the time.
Feel free to try to solve it first. When you’re ready (or if you want to skip the solving part), watch the video below to see how I solve it.