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 a¤ects the outcome of the auction. We also study the impact of budget caps on total bids. We show that both of

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... hese features, which are common in practice but absent from the previous literature, matter signi...cantly in determining the outcome of the auctions. JEL classi...cation: C62,C63,C72,D44,D82 Leininger (1991) contains results very similar to most of the results in this paper. Nevertheless, because there are some small di¤erences in the model and the exposition is di¤erent, we are making this manuscript available, while emphasizing that versions of the main results herein were previously published by Leininger (1991). y Dekel is at the