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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

Nash Equilibrium

Lectures in Microeconomics-Charles W. Upton

modeling an industry
Modeling an Industry
  • Competitive Industry – Many Firms
  • Monopoly – One Firm
  • Duopoly (Oligopoly) – A Few Firms

Nash Equilibrium

modeling an industry3
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
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 problems5
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

nash equilibrium6
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
A Nash Equilibrium
  • Each person or firm is acting rationally
  • No one believes his actions will change other decisions

Nash Equilibrium

a nash equilibrium8
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
Cournot

qA = 45 – (1/2)qB

qB = 45 – (1/2)qA

Nash Equilibrium

cournot10
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

cournot11
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

the bertrand model
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

the bertrand model13
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
Some Questions about Nash Equilibrium
  • Nash Equilibrium is useful for studying problems where there are just a couple of players.

Nash Equilibrium

this slide left blank
This slide left blank

Nash Equilibrium

nash and duopolies
Nash and Duopolies
  • Does there have to be a Nash Equilibrium? No

Nash Equilibrium

nash and duopolies17
Nash and Duopolies
  • Does there have to be a Nash Equilibrium?
  • Does there have to be only one Nash Equilibrium? No

Nash Equilibrium

slide18
End

©2003 Charles W. Upton

Nash Equilibrium

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