Winner’s Optimal Reimbursement in Contest

Abstract EN

This paper explores a designer-optimal reimbursement scheme in all-pay auctions with winner’s reimbursement.

Assuming the reimbursement is a linear function of the cost of effort, we obtain analytical solutions for the contestants’ symmetrical equilibrium effort and the contest organizer’s expected revenue.

We show that if the effort cost function is concave, the optimal reimbursement scheme is to return the full cost to the winner.

On the contrary, if the effort cost function is convex, the optimal reimbursement scheme is not to compensate the winner.

Moreover, we find that the organizer’s expected revenue may increase or decrease as the number of contestants increases when the winner is fully reimbursed.