On the optimal design of all-pay auctions

We consider the optimal design of complete-information all-pay auctions with multiple heterogeneous players when a designer can manipulate contestants’ relative competitiveness by imposing identity-dependent treatments. Three types of instruments are considered: (i) multiplicative biases that assign individualized weights to each contender’s effective effort, (ii) additive headstarts that directly add to it, and (iii) tie-breaking rule. We show that in general, both multiplicative biases and additive headstarts will be used for contest design. Moreover, the contest designer is able to induce every allocation of the prize while achieving full surplus extraction with an appropriately designed contest rule and tie-breaking rule.