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All-Pay Auctions With Budget Constraints: The Two Bidder Case

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Executive Summary

Consider an all-pay auction with interdependent, affiliated valuations and private budget constraints. The authors characterize a symmetric equilibrium for the case of two players. In contrast with the second-price auction, making budgets more severe can depress the bids of unconstrained bidders. Suppose firms are lobbying for a lucrative government contract to supply some product. Clearly, the contract's net value has an idiosyncratic component as each firm's production costs may differ. On the other hand, each firm also has a privately known limit on how much it is able to spend on lobbying. Perhaps the management approves of small restaurant meals but large expenditures or bribes are morally too much to stomach.

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