Nash Equilibriums // How to use Game Theory to render your opponents indifferent

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Nash Equilibria are one of the most powerful ideas in Game Theory, this was the subject of the movie Beautiful Mind. Given a normal form game, a mixed Nash Equilibrium is a choice of mixed strategy (i.e. probabilistic) for each player where no player can unilaterally improve their expected payoff. Incredibly, every such normal form game (with a finite number of players who can each choose from a finite number of pure strategies,) has a Nash Equilibrium! In this video I show you how to use pay-off matrices to computed the Expected Payoff aka Expectation Value for each action and use the Principle of Indifference to arrive at the Nash Equilibrium. We see two Nash Equilibrium examples, one from the football aka soccer world and one from economics with two firms in competition for a new market.

0:00 Intro to Nash Equilibriums
0:56 Football Example Intuitively
2:59 Mixed Strategies & the Indifference Principle
4:00 Expected Payoff
4:55 Definition of Nash Equilibrium
5:32 Nash Existence Theorem
6:06 Football Example Mathematically
10:14 Economics Example
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