We consider discrete versions of first-price auctions. We present a condition on beliefs about players' values such that, with any fixed finite set of possible bids and sufficiently many players, only bidding the bid closest from below to one's true value survives iterative deletion of bids that...

We study all-pay auctions (or wars of attrition), where the highest bidder wins an object, but all bidders pay their bids. We consider such auctions when two bidders alternate in raising their bids and where all aspects of the auction are common knowledge including bidders' valuations. We...

Auction models are convenient abstractions of informal price-formation processes that arise in markets for assets or services. These processes involve frictions such as bidder recruitment costs for sellers, participation costs for bidders, and limitations on sellersícommitment abilities. This...

This paper analyzes a common-value, first-price auction with state-dependent participation. The number of bidders, which is unobservable to them, depends on the true value. For participation patterns with many bidders in each state, the bidding equilibrium may be of a "pooling" type - with high...