Philip Brookins

Contests with group size uncertainty: Experimental evidence

In many contest situations, the number of participants is not observable at the time of investment. We design a laboratory experiment to study individual behavior in Tullock (lottery) contests with group size uncertainty. There is a fixed pool of n potential players, each with independent probability q of participating. As shown by Lim and Matros (2009; Games and Economic Behavior, vol. 67, pp. 584-597), the unique symmetric equilibrium investment level in this setting can exhibit nonmonotonicity with respect to both n and q. We independently manipulate each of the parameters and test the implied comparative statics predictions. Our results provide considerable support for the theory, both in terms of comparative statics and point predictions. Most surprisingly, we find no evidence of overbidding in treatments where there is a nontrivial probability that group size is one. This stands in stark contrast to the robust overbidding observed in experimental contests with deterministic group size. We propose a one-parameter model that incorporates nonlinear probability weighting and a modified version of joy of winning, which we call Constant Winning Aspirations (CWA), and show that it neatly organizes all of our results. The CWA model applies to a broad range of contexts and may be used to explain existing evidence on the differences in overbidding across many other contest and auction experiments.

Indefinitely Repeated Contests: An Experimental Study

We experimentally explore indefinitely repeated contests. Theory predicts more cooperation, in the form of lower expenditures, in indefinitely repeated contests with a longer expected time horizon, yet our data do not support this prediction. Theory also predicts more cooperation in indefinitely repeated contests compared to finitely repeated contests of the same expected length, but we find no significant difference empirically. When controlling for risk and gender, we actually find significantly higher long-run expenditure in some indefinite contests relative to finite contests. Finally, theory predicts no difference in cooperation across indefinitely repeated winner-take-all and proportional-prize contests. We find significantly less cooperation in the latter, because female participants expend more on average than their male counterparts in our data. Our paper extends the experimental literature on indefinitely repeated games to contests and, more generally, contributes to an infant empirical literature on behavior in indefinitely repeated games with “large” strategy spaces.