We show existence of equilibria in istributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of quilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing...

We consider discontinuous games with incomplete information. Auctions are a leading example. With standard tie breaking rules (or more generally, sharing rules), these games may not have equilibria. We consider sharing rules that depend on the private information of players. We show that there...

We consider discriminatory auctions for multiple identical units of a good. Players have private values, possibly for multiple units. None of the usual assumptions about symmetry of players' distributions over values or of their equilibrium play are made. Because of this, equilibria will...