Consider the toy problem of section 18.2. Imagine that the government institutes the following procedure: The two firms are asked to bid (simultaneously and independently) on the prices they will charge. They may not name a price greater than 4 or less than zero. (Of course, each knows its own unit cost when it does this.) If they name the same price, the order is split between them. If they name a different price, the order is given entirely to the firm naming the lower price. In both cases, the firm is paid per unit what it bids.
(a) If we construct from this mechanism the corresponding game (between the firms) of incomplete information, does the game have a pure strategy Nash equilibrium?
(b) If not, can you find a symmetric mixed strategy equilibrium?
(c) If you find any equilibrium, what is the corresponding direct revelation mechanism?