Burning Out in Sequential Elimination Contests

Abstract

Is it rational for contestants in a sequential elimination contest to expend all their efforts in earlier stages, get burnt out, and have nothing to offer in subsequent stages? This paper identifies three properties of sequential elimination contests which result in burning out: (i) a constraint on aggregate effort across stages or rounds (ii) extreme high-powered incentives in earlier rounds, and (iii) the playing field is even; no contestant is outstanding. I present a model which captures these three features. Burning out is shown to be an equilibrium rational behavior although the ultimate prize is won only if a contestant is successful in all stages including the last stage. I find two burning-out equilibria: a full burning-out equilibrium in which all the contestants burn out and a partial burning-out equilibrium in which some contestants do not burn out. I discuss some applications such as boxing contests, salary caps in the NBA, and incentives in academia.

Keywords: all-pay auction, burning out, caps, sequential elimination contests

JEL Classification: D44, D72