All–Pay Auctions with Variable Rewards

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Abstract

We study all–pay auctions with variable rewards under incomplete information. In standard models, a reward depends on a bidder’s privately known type; however, in our model it is also a function of his bid. We show that in such models there is a potential for paradoxical behavior where a reduction in the rewards or an increase in costs may increase the expected sum of bids or alternatively the expected highest bid.

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