Dynamic Win Effects in Sequential Contests

Abstract

We consider a principal who faces many identical competitors, and who can distribute a prize fund over two consecutive contests. The winner of contest one gains an advantage in contest two where his effort is more productive than all rivals. We identify a tipping point for the productivity parameter, below which it is optimal for an effort-maximizing principal to place the whole prize in the second contest. Above this level, a single symmetric contest is preferred. The institution chosen depends inextricably upon the number of competitors and their valuation of future gains and costs. We identify the optimal setting of the productivity parameter, showing that introducing asymmetry can increase total efforts by as much as one quarter compared to a single symmetric contest.