“Reverse” nested lottery contests

Abstract

This paper proposes a multi-prize “reverse” nested lottery contest model, which can be viewed as the “mirror image” of the conventional nested lottery contest of  Clark and Riis (1996a). The reverse-lottery contest model determines winners by selecting losers based on contestants’ one-shot effort through a hypothetical sequence of lotteries. We provide a microfoundation for the reverse-lottery contest from a perspective of (simultaneous) noisy performance ranking and establish that the model is underpinned by a unique performance evaluation rule. We further demonstrate that the noisy-ranking model can be interpreted intuitively as a “worst-shot” contest, in which contestants’ performances are evaluated based on their most severe mistakes. The reverse-lottery contest model thus depicts a great variety of widely observed competitive activities of this nature. A handy closed-form solution for a symmetric equilibrium of the reverse-lottery contest is obtained. We show that the winner-take-all principle continues to hold in reverse-lottery contests. Moreover, we find that a reverse-lottery contest elicits more effort than a conventional lottery contest whenever the prizes available to contestants are relatively scarce.