A seller with two items x and y considers running an auction. There are two potential bidders A and B with valuations:

vA(x,y) = 100, vA(x) = vA(y) = 0. vB(x,y) = 0, vB(x) = vB(y) = 75.

The spectrum auction may be an example. The government is selling the rights to transmit cell-phone signals over specic bands in NYC (x) and Boston (y). A large nation-wide cellphone service provider (A) believes that it is only worthwhile if they get the rights to both cities. A small provider (B) wants the right for only one city, as it is not capable of serving both cities.

(a) Suppose the seller runs a modied rst-price auction. Each bidder submits bids (i.e., three valuations, one for each item or the package), then the seller chooses the revenue-maximizing assignment, and the bidder pays her bid for an item, or the package, given by the seller. Would bidders submit their true valuations? Find any equilibrium bids in this example. (b) Suppose that the seller runs the VCG auction. Find the resulting allocation and each bidder's payments.