On Contests with Costly and Stochastic Entry

*Qiang Fu
Department of Business Policy, National University of Singap

Qian Jiao
Department of Economics, National University of Singapore

Jingfeng Lu
Department of Economics, National University of Singapore

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     Last modified: November 28, 2010
     Presentation date: 03/12/2011 2:45 PM in NH 1150, Session D
     (View Schedule)

Abstract
This paper studies imperfectly discriminatory contests with costly and endogenous entries. A fixed pool of potential bidders may enter a contest to compete for an indivisible prize. Entry incurs an irreversible fixed cost. They then bid for the prize after entry. The game exemplifies a two-dimensional discontinuous game (Dasgupta and Maksin, 1986). We establish that there exists a symmetric equilibrium in the entry-bidding game, where all potential bidders enter with a probability. We further identify a sufficient condition under which participating bidders play pure bidding strategy after entry. Based on the equilibrium result, we explore two main issues on optimal contest design. First, we investigate how the level of accuracy in the winner selection mechanism (i.e. the level of discriminatory power in Tullock rent-seeking contests) affects the expected overall bid. We find the relationship is non-monotonic. The contest designer may benefit from a noisier contest, which elicits the optimal amount of overall bid. Further we consider the optimal disclosure policy of the contest. That is, we ask whether it pays for the contest designer to disclose the actual
number of participants if she can observe it. We find that whenever bidders bear strictly convex bidding costs, the contest organizer prefers to conceal the actual number of participants to entrants, when the contest is sufficient noisy. However, the results are ambiguous otherwise.