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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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Nash Equilibrium

Lectures in Microeconomics-Charles W. Upton


Modeling an Industry

  • Competitive Industry – Many Firms

  • Monopoly – One Firm

  • Duopoly (Oligopoly) – A Few Firms

Nash Equilibrium


Modeling an Industry

  • Competitive Industry – Many Firms

  • Monopoly – One Firm

  • Duopoly (Oligopoly) – A Few Firms

    • Cournot

    • Bertrand

    • Might there be other approaches?

Nash Equilibrium


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


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


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


A Nash Equilibrium

  • Each person or firm is acting rationally

  • No one believes his actions will change other decisions

Nash Equilibrium


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


Cournot

qA = 45 – (1/2)qB

qB = 45 – (1/2)qA

Nash Equilibrium


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


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


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


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


Some Questions about Nash Equilibrium

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

Nash Equilibrium


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Nash Equilibrium


Nash and Duopolies

  • Does there have to be a Nash Equilibrium? No

Nash Equilibrium


Nash and Duopolies

  • Does there have to be a Nash Equilibrium?

  • Does there have to be only one Nash Equilibrium? No

Nash Equilibrium


End

©2003 Charles W. Upton

Nash Equilibrium


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