We study all-pay contests under incomplete information where the reward is a function of the contestant's type and effort. We analyse the optimal reward for the designer when the reward is either multiplicatively separable or additively separable in effort and type. In the multiplicatively...

We study all-pay contests in which there is a positive probability of a tied outcome. We analyse both one-stage contests and multi-stage contests with tie-breaks. We demonstrate that in symmetric two-player contests, the designer does not have an incentive to award a prize in a case of a tie....

According to the so-called Exclusion Principle (introduced by Baye et alii, 1993), it might be profitable for the seller to reduce the number of fully-informed potential bidders in an all-pay auction. We show that it does not apply if the seller regards the bidders’ private valuations as...

We show that the seller’s optimal reserve price in an all-pay auction with complete information is higher than in a standard auction. We use our results to re-consider some findings of the literature that models lobbying games as all-pay auctions. In particular, we show that the so-called...

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...

We study a college admissions problem in which colleges accept students by ranking students' efforts in entrance exams. Students' ability levels affect the cost of their efforts. We solve and compare the equilibria of 'centralized college admissions' (CCA) where students apply to all colleges...

As a selling mechanism, auctions have acquired a central position in the free market economy all over the globe. This development has deepened, broadened, and expanded the theory of auctions in new directions. This chapter is intended as a selective update of some of the developments and...

We study cheap-talk pre-play communication in the static all-pay auctions. For the case of two bidders, all correlated and communication equilibria are payoff equivalent to the Nash equilibrium if there is no reserve price, or if it is commonly known that one bidder has a strictly higher value....

We study a college admissions problem in which colleges accept students by ranking students’ efforts in entrance exams. Students’ ability levels affect the cost of their efforts. We solve and compare the equilibria of “centralized college admissions” (CCA) where students apply to all...