Investment and endogenous efficiency in a contest

Abstract

Contests are ubiquitous but do not happen in a vacuum. Rivals can prepare themselves for the contest to improve their ultimate chance of victory. Two contestants with different prize values play an all-pay auction and can invest to improve the efficiency of their own effort in the contest. We show that at most one player will invest, and that two asymmetric pure-strategy equilibria exist depending upon the identity of the investor. If the high-value player invests, then investment reinforces the initial asymmetry; investment by the low-value player turns the tables on the initially advantaged rival. The investment opportunity moves competition away from the contest, resulting in less expected contest effort than would occur without investment.