Effect of reimbursement on all-pay auction

We study all-pay auctions with winners' reimbursement. This study is conducted under incomplete information with non-linear effort functions. We show that when the cost of effort is concave, the expected revenue in all-pay auctions with reimbursement is higher than the expected revenue in all-pay auctions without reimbursement. However, when the cost of effort is convex, the expected revenue in all-pay auctions without reimbursement is higher. The results of this paper supply a justification to apply reimbursement in contests as part of a mechanism to increase expected revenue. This is especially true in contests where applying new technologies results in decreasing the marginal costs of efforts.