Skewing the odds: Strategic risk taking in contests

We study contests where, subject only to a capacity constraint on mean performance, contestants compete for identical prizes by choosing random performance levels. The capacity constraint combined with the rank-contingent rewards makes winsmall/lose-big strategies optimal. Equilibrium strategies are generally skewed but never risk maximizing. When capacity is known and symmetric, we derive a closed-form solution for the game and analyze the effects of contest selectivity and size on equilibrium outcomes. We next consider contests where capacity is private information and show that, contrary to the risk-taking-and-ruin intuition, weak contestants do not always gamble on high-risk strategies. In fact, when the capacities of weak and strong contestants differ sufficiently, weak contestants choose low-variance performance distributions that never top strong contestants’ performance, ensuring that the equilibrium is perfectly selection efficient. Finally, we consider the implications of our analysis for mutual fund tournaments, R&D competition, and stochastic contests.