will be shared exogenously, and the rest proportionally. We examine the efficiency properties of such rules, compare them …

for externalities, substitutabilities and complementarities. Firms' cost parameter is private information and is … independently distributed across firms. Externalities are type dependent. This has two consequences: first, even though the private …, which makes the use of variational methods possible. A further consequence of having type-dependent externalities, which …

, allocative externalities, and two-sided trading. Given no externalities, further, all mixed-strategy equilibria in these auctions …