affected by the production technology. The general message is that making contest par- ticipants more heterogeneous can increase equilibrium effort. These findings contradict certain “standard” results known from the Tullock contest and the Lazear-Rosen tourna- ment. Thus, the comparative statics results derived from those standard models are not representative of the conclusions derived in the more general model.
To shed further light on our results, we also provide two extensions to our main anal- ysis. In a first extension, we study the behavior in contests when the number of players $n$ is greater than two and show that the existence of a symmetric equilibrium, and the interpretation for the two-player case, extend to the $n$-player case when players have identical skill distributions. We also show that, for a specific class of skill distributions, a symmetric equilibrium exists when $n - 1$ identical players compete against a player who has a higher expected skill. Moreover, we show that increasing the number of contest- tants can increase equilibrium effort, exploiting the fact that a contest with $n > 2$ players can be interpreted as a two-player contest in which every player competes against the strongest (i.e., the highest order statistic) of his or her opponents.¹
In a second extension, we investigate the robustness of our results with respect to the assumption of symmetric uncertainty by analyzing the consequences of letting players be privately informed about their skills. In this case, equilibria are in general not symmetric, but focusing on symmetric players, we are able to draw interesting parallels with respect to our baseline case, highlighting the role of our general production technology in influencing the marginal incentive to exert effort.
We also discuss the implications of our findings for optimal team composition and certain real-world applications in the context of labor and personnel economics. For instance, our finding that efforts can increase if the skill distribution of one of the competing players becomes more uncertain (in the sense of second-order stochastic dominance) has several interesting managerial implications. It indicates that contest organizers might wish to increase the uncertainty regarding the skills of certain players in order to induce higher effort. In a worker-firm context, employers could achieve this by, for instance, hiring a worker for whom little prior information is available, or a minority worker with a skill level drawn from a distribution that generally tends to be more uncertain (as argued, e.g., by Bjerk 2008). This means that having diverse teams might be desirable from an employer's point of view.
¹This result can be understood by the fact that as the number of contestants increases, the strongest opponents grow stronger in the sense of first-order stochastic dominance, allowing us to apply our results from the two-player case.