Journal of Mathematical Economics
Volume 50, January 2014, Pages 128-140
"Reverse" Nested Lottery Contests
QiangFua JingfengLub ZheweiWangc
a Department of Strategy and Policy, National University of Singapore, 15 Kent Ridge Drive, 119245, Singapore
b Department of Economics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore
c School of Economics, Shandong University, 27 Shanda Nanlu, Jinan, 250100, China
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.
