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ECON 4320 TTU Nash Equilibrium Expected Payoff & Mixed Strategy Worksheet

Firm A and Firm B sell identical versions of the textbook “Intermediate Microeconomics”

As in the example in class, total market demand for the book is:

The inverse demand function is therefore

Where is total market production. That is,

As a result the

The difference between this example and the example in class is that the two firms have different costs. Firm A has the same costs as in the example in class. However, marginal costs are higher for firm B

Note: Firm A’s best response should be a function of

Note: Firm A’s best response should be a function of

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• 2.(18 points) Mixed strategy Nash equilibrium – Chicken
• (18 points) Mixed strategy Nash equilibrium – Cartel (Prisoner’s Dilemma-type Game)

Consider the game below

See Lecture 24

How to Slides (How to solve for mixed strategy Nash equilibrium)

 Firm B Firm A Swerve Drive Straight Swerve A: B: A: B: Drive Straight A: B: A: B:

A.(3 points) Underline Firm A’s best response to each of firm B’s strategies

B.(3 points) Underline Firm B’s best response to each of firm A’s strategies

C.(3 points) Are there any pure strategy Nash Equilibrium in this game? If so, what is it/are they.

D.(3 points) Assuming there is a mixed strategy Nash Equilibrium, calculate the probability that Firm A swerves (p)

E.(3 points) Assuming there is a mixed strategy Nash Equilibrium, calculate the probability that Firm B swerves (q)

F.(3 points) Are there any mixed strategy Nash Equilibrium? If so, what is it/are they

.

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Consider the game below

See Lecture 24

How to Slides (How to solve for mixed strategy Nash equilibrium)

 Firm B Firm A Stick to Agreement Cheat Stick to Agreement A: \$30 B: \$30 A: \$0 B: \$40 Cheat A: \$40 B: \$0 A: \$5 B: \$5

A.(3 points) Underline Firm A’s best response to each of firm B’s strategies

B.(3 points) Underline Firm B’s best response to each of firm A’s strategies

C.(3 points) Are there any pure strategy Nash Equilibrium in this game? If so, what is it/are they.

D.(3 points) Assuming there is a mixed strategy Nash Equilibrium, calculate the probability that Firm A sticks to the agreement (p)

E.(3 points) Assuming there is a mixed strategy Nash Equilibrium, calculate the probability that Firm B sticks to the agreement (q)

F.(3 points) Are there any mixed strategy Nash Equilibrium? If so, what is it/are they.

.

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