In Chapter 23, we discussed first, second and third degree price discrimination by a monopolist. Such pricing decisions are strategic choices that can be modeled using game theory — which we proceed to do here. Assume throughout that the monopolist can keep consumers who buy at low prices from selling to those who are offered high prices.
A: Suppose a monopolist faces two types of consumers — a high demand consumer and a low demand consumer. Suppose further that the monopolist can tell which consumer has low demand and which has high demand; i.e. the consumer types are observable to the monopolist.
(a) Can you model the pricing decisions by the monopolist as a set of sequential games with different consumer types?
(b) Suppose the monopolist can construct any set of two-part tariffs —i.e. a per-unit price plus fixed fee for different packages. What is the sub game perfect equilibrium of your games?
(c) True o*/r False: First degree price discrimination emerges in the sub game perfect equilibrium but not in other Nash equilibria of the game.
(d) How is this analysis similar to the game in exercise 24.5?
(e) Next, suppose that the monopolist cannot charge a fixed fee but only a per-unit price — but he can set different per-unit prices for different consumer types. What is the sub game perfect equilibrium of your games now?
B: Next, suppose that the monopolist is unable to observe the consumer type but knows that a fraction ρ in the population are low demand types and a fraction (1−ρ) is high demand types. Assume that firms can offer any set of price/quantity combinations.
(a) Can you model the price setting decision by the monopolist as a game of incomplete information?
(b) What is the (sub game) perfect Bayesian equilibrium of this game in the context of concepts discussed in Chapter 23? Explain.