Question
Consider a seller of a used car and a potential buyer of that car. Suppose that quality of the car, , is drawn from a
Consider a seller of a used car and a potential buyer of that car. Suppose that quality of the car, , is drawn from a uniform distribution on [0, 1]. This quality is known to the seller, but not to the buyer. Suppose that the buyer can make an offer p [0, 1] to the seller, and the seller can then decide whether to accept or reject the buyer's offer. The seller's payoff is p if the offer is accepted and if the offer is rejected. The buyer's payoff is a + b p if the offer is accepted and 0 if the offer is rejected. Assume that a (0, 1), b (0, 2), and a + b > 1. Give an example of a strategy for each player. Find the pure strategy Bayesian Nash equilibrium/equilibria of this game and comment on whether efficiency is achieved in equilibrium.
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