We study all-pay auctions with budget-constrained bidders who have access to fair insurance before bidding simultaneously over a prize. We characterize a unique equilibrium for the special cases of two bidders and one prize, show existence and a heuristic for finding an equilibrium in the case...

The paper characterizes the mixed-strategy equilibria in all-pay auctions with endogenous prizes that depend positively on own effort and negatively on the effort of competitors. Such auctions arise naturally in the context of investment games, lobbying games, and promotion tournaments. We also...

This paper analyzes how all-pay auctions with endogenous prizes can be used to provide effort incentives. We show that wide classes of effort distributions can be implemented as equilibrium outcomes of such games. We also ask how all-pay auctions have to be structured so as to induce high...