What is game theory

Question

Assignment:

Part A

1. What is oligopoly? What is duopoly?

2. What is game theory? What is its role in explaining the behavior of an oligopolist or a duopolist? How do we determine the equilibrium strategies in a duopoly?

3. Cournot model: Quantity competition in simultaneous move homogeneous product duopoly- explain in words.

The market for bricks consists of two firms that produce identical products. Competition in the market is such that each of the firms simultaneously and independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 has a patented technology that provides it with a cost advantage over firm 1. A recent study found that the market demand curve faced by the two firms is P = 2:1- 1/40000 (x + y); and costs are C₁(x) = 0:25x and C₂(y) = 0:2y; where firm 1 produces x units and firm 2 produces y units of bricks.

(a) Determine the reaction function for each firm.

(b) How much output will each firm produce in equilibrium? At what price? How much will be the equilibrium profit for each firm?

4. Stackelberg model: Quantity competition in sequential move homogeneous product duopoly explain in words.

Refer to the information given before part a of Question 3. Suppose firm 2 is a "naive" Cournot duopolist so that firm I can act as a Stackelberg leader.

(a) What level of output will each one of them produce in equilibrium? At what price? How much will be the equilibrium profit for each firm?

(b) Ignoring antitrust considerations, would it be profitable for firm 1 to merge with firm 2? Explain.

Part B

5. Bertrand model: Price competition in simultaneous move homogeneous product duopoly explain in words.

Consider the brick producers again. This time, each firm simultaneously and independently picks the price. Since the product is homogeneous, the consumer buys from the producer offering at a cheaper price. The market demand curve faced by the two firms is P = 2.1 -1/40000 (x + y); and costs are C₁(x) = 0:2x and C₂(y) = 0:2y; where firm 1 produces x units and firm 2 produces y units of bricks. What price will each one of them charge in equilibrium? How much will be the profit?

6. Price competition in simultaneous move differentiated product duopoly:

There are only two food trucks in a town. Their menus are not identical, but not totally different either. The price for each entree in a truck is the same. The trucks pick their prices and sell according to their demand. The demand curve faced by truck 1 is given by: x = 113 25p₁ + 20p₂ and by truck 2 is given by: y = 100 25p₂ + 20p₁: The costs are C₁(x) = 3x and C₂(y) = 2:4y; where Örm 1 serves x consumers and firm 2 serves y consumers.

(a) Determine the reaction function for each truck.

(b) How much output will each truck produce in equilibrium? At what price? How much will be the equilibrium profit for each truck?