Game Theory 101: Mixed Strategy Nash Equilibrium (Part 1)
What can we learn from The Princess Bride?
The mixed strategy Nash equilibrium is one of the most fundamental concepts within game theory and solving it can yield significant insights into strategic behaviors. In this video, we learn about the mixed strategy Nash equilibrium and see an example from the movie "The Princess Bride", where mixing strategies is key.
As we learned earlier, a Nash equilibrium occurs when the players of a game see no incentive to move unilaterally from a particular outcome - it’s a stable point in the game. To this point, we’ve studied only what are called “pure strategy” Nash equilibria - games where a player would want to take a particular action 100% of the time.
That won’t be the case for many games, however. Take, for example, penalty kicks in soccer.
A penalty kick situation will not have a pure strategy Nash equilibrium. The goalie will have an incentive to jump to whatever side the kicker is kicking towards and the kicker will have an incentive to kick away from the side the goalie jumps towards. And if one player did something 100% of the time, they would be easily exploited.
With game theory, we can solve for the exact percentage of the time players - when playing optimally - would take each action, and that is the mixed strategy Nash equilibrium.
We get our introduction to the mixed strategy Nash equilibrium with this video - which covers a famous scene in The Princess Bride.
More on the mixed strategy Nash equilibrium will be coming soon, so stay tuned!