Exercise BCS 75 (Multiobject Auction) There is a seller who has one unit each of three different objects to sell. We name these objects a, b, and c. There are two potential buyers who have different valuations for these objects. These valuations are given in the following table:
buyer's value objects
a / b / c
v1 16 / 10 / 20
v2 18 / 16 / 12
For instance, buyer 1's value for object b is 10 while buyer 2's value for object b is 16.
The seller considers selling these objects through second-price auctions. In particular, he considers two kinds of sales. First, he may auction off these objects with three different second-price auctions, one for each object. Call this the "single-object" sale. Second, he considers two different second-price auctions, one for the bundle of objects fb; cg (i.e., both objects b and c are sold together in the same auction) and one for the object a. Call
this the "bundled-object" sale.
We assume that if a buyer buys more than one object, then his value for these objects is simply the sum of the values for each object he buys. We also assume that buyers bid according to an equilibrium in which no bid is weakly dominated. The seller prefers the sale that gives him the highest revenue. Should the seller use the "single-object" sale or the "bundled-object" sale? Explain your answer in detail.
Suppose that the Federal Trade Commission (FTC) wants to regulate the sale so as to maximize eciency. In particular, the goal of the FTC is to allow only sales that ensure that for each object the buyer with the highest value obtains the object. Will the FTC
require the seller to use the "single-object" sale or the "bundled-object" sale? Explain your answer in detail.