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Nash Equilibrium

Nash Equilibrium. Modeling an Industry. Competitive Industry – Many Firms Monopoly – One Firm Duopoly (Oligopoly) – A Few Firms. Modeling an Industry. Competitive Industry – Many Firms Monopoly – One Firm Duopoly (Oligopoly) – A Few Firms Cournot Bertrand

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Nash Equilibrium

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  1. Nash Equilibrium Lectures in Microeconomics-Charles W. Upton

  2. Modeling an Industry • Competitive Industry – Many Firms • Monopoly – One Firm • Duopoly (Oligopoly) – A Few Firms Nash Equilibrium

  3. Modeling an Industry • Competitive Industry – Many Firms • Monopoly – One Firm • Duopoly (Oligopoly) – A Few Firms • Cournot • Bertrand • Might there be other approaches? Nash Equilibrium

  4. Different Problems • A can build an expensive or cheap car. • B can build an expensive or cheap car. • There are four possible outcomes (E,E), (E,C), (C,E), (C,C) • What will happen? Nash Equilibrium

  5. Different Problems • Firm A can build an expensive or a cheap car. • Firm B can build an expensive of cheap car. • There are four possible outcomes (E,E), (E,C), (C,E), (C,C) • What will happen? Which, if any of those outcomes is a Nash Equilibrium? Nash Equilibrium

  6. Firms must end up at a Nash Equilibrium, named after John Nash A Nash Equilibrium Each person or firm is acting rationally Nash Equilibrium Nash Equilibrium

  7. A Nash Equilibrium • Each person or firm is acting rationally • No one believes his actions will change other decisions Nash Equilibrium

  8. A Nash Equilibrium • Each person or firm is acting rationally • No one believes his actions will change other decisions • No one has an incentive to change Nash Equilibrium

  9. Cournot qA = 45 – (1/2)qB qB = 45 – (1/2)qA Nash Equilibrium

  10. Cournot qA = 45 – (1/2)qB qB = 45 – (1/2)qA Does the Cournot model predict we will end up at a Nash Equilibrium? Yes Nash Equilibrium

  11. Cournot qA = 45 – (1/2)qB qB = 45 – (1/2)qA • Each person or firm is acting rationally • No one believes his actions will change other decisions • No one has an incentive to change Nash Equilibrium

  12. Demand function is as shown. Firm with lowest bid gets all the market. In case of tie, firms split market MC = 0 The Bertrand Model Does the Bertrand Model predict we will end up at a Nash Equilibrium? Yes D Nash Equilibrium

  13. Demand function is as shown. Firm with lowest bid gets all the market. In case of tie, firms split market MC = 0 The Bertrand Model • Each person or firm is acting rationally • No one believes his actions will change other decisions • No one has an incentive to change D Nash Equilibrium

  14. Some Questions about Nash Equilibrium • Nash Equilibrium is useful for studying problems where there are just a couple of players. Nash Equilibrium

  15. This slide left blank Nash Equilibrium

  16. Nash and Duopolies • Does there have to be a Nash Equilibrium? No Nash Equilibrium

  17. Nash and Duopolies • Does there have to be a Nash Equilibrium? • Does there have to be only one Nash Equilibrium? No Nash Equilibrium

  18. End ©2003 Charles W. Upton Nash Equilibrium

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