Optimal Contest Design for Simple Agents

Incentives are more likely to elicit desired outcomes when they are designed based on accurate models of agents’ strategic behavior. A growing literature, however, suggests that people do not quite behave like standard economic agents in a variety of environments, both online and offline. What consequences might such differences have for the optimal design of mechanisms in these environments? In this article, we explore this question in the context of optimal contest design for simple agents—agents who strategically reason about whether or not to participate in a system, but not about the input they provide to it. Specifically, consider a contest where n potential contestants with types (qi, ci) each choose between participating and producing a submission of quality qi at cost ci, versus not participating at all to maximize their utilities. How should a principal distribute a total prize V among the n ranks to maximize some increasing function of the qualities of elicited submissions in a contest with such simple agents? We first solve the optimal contest design problem for settings where agents have homogenous participation costs ci = c. Here, the contest that maximizes every increasing function of the elicited contributions is always a simple contest, awarding equal prizes of V/j* each to the top j*=V/c − Θ(√V/(c ln (V/c))) contestants. This is in contrast to the optimal contest structure in comparable models with strategic effort choices, where the optimal contest is either a winner-take-all contest or awards possibly unequal prizes, depending on the curvature of agents’ effort cost functions. We next address the general case with heterogenous costs where agents’ types (qi, ci) are inherently two dimensional, significantly complicating equilibrium analysis. With heterogenous costs, the optimal contest depends on the objective being maximized: our main result here is that the winner-take-all contest is a 3-approximation of the optimal contest when the principal’s objective is to maximize the quality of the best elicited contribution. The proof of this result hinges around a “subequilibrium” lemma establishing a stochastic dominance relation between the distribution of qualities elicited in an equilibrium and a subequilibrium—a strategy profile that is a best response for all agents who choose to participate in that strategy profile; this relation between equilibria and subequilibria may be of more general interest.