Contests with a stochastic number of players

Abstract

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p ≤ 1 of participating. A unique symmetric equilibrium is found for any n and p and its properties are analyzed. In particular, we show that for a fixed n > 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post overdissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.

Repeated Contests with Asymmetric Information

“…Formally, I assume that each contestant has either a high or a low valuation, where the low valuation is zero. The model describes situations where the contestants do not know whether or not they face an active competitor, as in Myerson and Wärneryd (2006), Münster (2006), and Lim and Matros (2007). The valuations of the contestants are independent, but are constant over time.…”

Volunteering under population uncertainty

“…This increase can at least in part be traced back to individual risk preferences (e.g., Haviv and Milchtaich, 2012). Moreover, population uncertainty inuences equilibrium spending in contests theoretically and experimentally (Lim and Matros, 2009;Boosey et al, 2016). Further, even very well known economic results like the optimal pricing behavior in a Bertrand competition change with population uncertainty (Ritzberger, 2009).…”

On disclosure policy in contests with stochastic entry

“…Myerson and Wärneryd (2006) examined a contest with an infinite number of potential entrants. Both Münster (2006) and Lim and Matros (2010) assumed a finite pool of potential contestants. In their setting, each participating contestant enters the contest with a fixed and independent probability and the number of participating contestants follows a binomial distribution.…”

“…Münster (2006) focused on the impact of players' risk attitudes on the contestants' incentive to supply effort. In contrast, Lim and Matros (2010) considered a scenario with risk-neutral contestants.…”

“…The current study is most closely related to Lim and Matros (2010), who provide a complete account of the bidding equilibrium in a Tullock contest with a stochastic number of contestants. To the best of our knowledge, Lim and Matros (2010) are the first to study optimal disclosure policies in contests.…”