Question

Consider a two-person problem in which there is a single seller who owns an indivisible object and single potential buyer of the object Each agent has a value for the object that is known to him but not known to the other agent. The mechanism for (possible) trade is that each agent announces a price, and if the buyer's announcement is larger than the seller's announcement, the object is sold to the buyer at the seller's announced price. There is no trade if the buyer's announcement was smaller than the seller's. 

(a) Show that the buyer has a dominant strategy. 

(b) Suppose that both the buyer's value and the seller's value are uniformly distributed on the interval [0, 1] and that they are in- dependent. What is the seller's strategy in the Bayes equilibrium in which the buyer plays the strategy in part a.? 

(c) Suppose that the seller's value was in the interval [0, 1] but that the density function was f(vs) = 2vs. How would the seller's strategy change from your answer in part b.?

Answer 1