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Ecos3005: Tutorial 2

For discussion Week 3

Question 1:  Simultaneous move games

Consider the strategic situation of a penalty in a soccer game. The striker has the opportunity to shoot a penalty. The goalkeeper wishes to save the penalty. The striker has two choices: shoot left (L) or shoot right (R). The goalkeeper has two choices: dive left (L) or dive right (R). If the striker and goalkeeper both choose the same direction, the striker scores with probability 0.2. If they choose opposite directions, then the striker scores with probability 0.9.  The striker and goalkeeper must act at exactly the same time. This game can be represented in normal form as follows:

Goalkeeper

Left       Right

0.2, 0.8

0.9, 0.1

0.9, 0.1

0.2, 0.8

Question 2:  Simultaneous move games

Consider the following perturbed market entry game.

Double Bay Blue

Enter         Don’t

50, −50

150, 0

0, 100

0, 0

Find all the Nash equilibria to this game.

 

Question 3:  Sequential move games

Identify the Subgame perfect Nash equilibria to the game below.

1

Left           Right

2

 

Down

− 1 − 1

Question 4:  Monopoly and Perfect Competition

Demand for a particular drug is Q = 16P 2 .  The drug is protected by a patent, and is supplied by a monopolist with costs C(Q) =  +  (this cost does not include the R&D costs, just the manufacturing costs).

1. Is this industry a natural monopoly?

2. Calculate the equilibrium price, output and monopoly profits. Sketch them on a diagram.

3. Now the patent expires and anyone can produce the drug. Potential new entrants have the same cost function as the original monopolist. How many firms enter? What will be the long-run equilibrium price and quantity for the market as a whole?

4. Can you say whether society as a whole is worse off as a result of the monopoly market structure? Explain your answer, using a diagram.