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

Check out Brilliant ► https://brilliant.org/TreforBazett/ Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory. Game Theory Playlist ►    • Game Theory   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 14:45 Check out Brilliant.org/TreforBazett/ COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • How to solve ODEs with infinite series | I...   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems Actu...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography