Tractable Binary Contests

Abstract

Much of the work on multi-agent contests is focused on determining the equilibrium behavior of contestants. This capability is essential for the principal for choosing the optimal parameters for the contest (e.g., prize amount). As it turns out, many contests exhibit not one, but many possible equilibria, hence precluding contest design optimization and contestants’ behavior prediction. In this article, we examine a variation of the classic contest that alleviates this problem by having contestants make the decisions sequentially rather than in parallel. We study this model in the setting of a binary contest , wherein contestants only choose whether or not to participate, while their performance level is exogenously set. We show that by switching to the sequential mechanism not only does there emerge a unique equilibrium behavior, but also that the principal can design this behavior to be as good, and, at times, better, than any pure-strategy equilibrium of the parallel setting (assuming the principal’s profit is either the maximum performance or the sum of performances). We also show that in the sequential setting, the optimal prize, which is inherently a continuous parameter, can be effectively computed and reduced to a set of discrete values to be evaluated. The theoretical analysis is complemented by comprehensive experiments with people over Amazon Mechanical Turk. Here, we find that the modified mechanism offers great benefit for the principal in terms of an increased over-participation in the contest (compared to theoretical expectations). The effect on the principal average profit, however, depends on its goal in the contest—when benefiting from the maximum performance the modified mechanism results in increased average profit, while when benefiting from the sum of performances, it is preferred to stay with the original (parallel) contest.