Sequential Elimination Contests with All-Pay Auctions

By modeling contests as all-pay auctions, we study two-stage sequential elimination contests (SEC) under incomplete information, where only the players with top efforts in the first stage can proceed to the second and final stage to compete for prizes. Players have privately held type/ability information that impacts their costs of exerting efforts. We characterize players' Perfect Bayesian Equilibrium strategies and discover a somewhat surprising result: all players exert weakly lower efforts in the final stage of the SEC compared to those under a one-round contest, regardless of the number of players admitted to the final stage. This result holds under any multi-prize reward structure, any type distribution and cost function. As a consequence, in terms of the expected highest effort or total efforts of the final stage, the optimal SEC is equivalent to a one-round contest by letting all players proceed to the final stage.