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 ∈ (0, 1] 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.