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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

### 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

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