Jump Bidding and Budget Constraints in All-Pay Auctions and Wars of Attrition

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 analyze how the ability to "jump-bid," or raise bids by more than the minimal necessary increment affects the outcome of the auction. We also study the impact of budget caps on total bids. We show that both of these features, which are common in practice but absent from the previous literature, matter signi…cantly in determining the outcome of the auctions.