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## PowerPoint Slideshow about 'Nash Equilibrium' - elinor

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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 EquilibriumNash 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

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 ModelDoes 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?
- Does there have to be only one Nash Equilibrium? No

Nash Equilibrium

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