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GT3-NE - Nash equilibrium A set of strategies in which no...

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1 1 Nash Equilibrium UGBA 143: Game Theory and Business Decisions 2 Nash equilibrium A set of strategies in which no player would unilaterally switch to another alternative Previous examples: Prisoners’ Dilemma: both confess Location Game: both locate at midpoint Cournot Competition: charge a particular price 3 Recall Previous lectures: Elimination of dominated strategies All players choosing best responses (i.e. intersection point of best response curves) Uses of Nash Equilibrium: Descriptive: predict outcomes in strategic interactions Prescriptive: suggest an optimal strategy to adopt N.E. 4 Nash equilibrium Why should we believe in it? – Rational inference eliminates uncertainty – No reason for players not to play Nash Equilibrium – Focal point – Self-enforcing agreement – Stable social convention 5 A brief history… John Nash Princeton math PhD (1950) 8-page paper, 27-page dissertation Published in Proc. Nat. Acad. Sci. Main result: All games have a Nash equilibrium More tidbits: – One-line letter of recommendation: “This man is a genius.” – Princeton PhD at age 21, MIT tenure at age 29 – “most trivial result” – Economics Nobel Prize in 1994
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