Optimal Contest Design for Simple Agents

Abstract

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 ( q i , c i ) each choose between participating and producing a submission of quality q i at cost c i , 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 c i = 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 ( q i , c i ) 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.

Sketching an AI Marketplace: Tech, Economic, and Regulatory Aspects

“…Another approach could be to organize contests among AI developers for some pre-defined reward. However, contests and their corresponding reward incentives should be designed based on accurate models of AI developers' strategic behavior to elicit the desired outcomes [40]. Depending on the strategic behavior of the AI developers, different kinds of contests can be organized, e.g., contests that reward a fixed number of AI developers, contests that take the form of a tournament, or contests that award everything to the winner [41], [42].…”

Quality-Aware Pricing for Mobile Crowdsensing

“…knowledge" on the users' qualities and costs is available 2 , i.e. : the joint probability distribution of each user's type (q i , c i ) is known to the crowdsensing task owner [33], but the exact values of q i and c i are unknown. We will also drop this assumption and extend our algorithms in Sec.…”

Understanding Over Participation in Simple Contests

“…The underlying contest model used in our experimental design is similar to the one used by our prior work (Levy, Sarne, and Rochlin 2017) and by Ghosh and Kleinberg (2016) and Sarne and Lepioshkin (2017). Formally, the model considers a contest organizer and a set A = {A 1 , ..., A k } of k > 1 potential contestants.…”

“…Contests are organizational structures in which contestants spend costly efforts (e.g., time, resources) to win one or more prizes (Dechenaux, Kovenock, and Sheremeta 2015). Contest design, i.e., the set of rules that define a contest, had focused much interest in literature (Dasgupta and Nti 1998;Ghosh and Kleinberg 2016), differing primarily in the assumptions made in the underlying contest model (e.g., offering several prizes (Archak and Sundararajan 2009;Cavallo and Jain 2013) or using more than a single stage (most commonly in the form of a tournament) (Clark and Riis 1998;Gradstein and Konrad 1999)) and the contest organizer's goals (e.g., maximizing overall effort, best effort, fairness) (Lewenberg et al 2013).…”

“…For this purpose, we use a "simple" contest model in which contestants only need to strategize about participating in the contest (Ghosh and Kleinberg 2016;Levy, Sarne, and Rochlin 2017;Sarne and Lepioshkin 2017). This contest model (and in particular the fact that a contestant's strategy is fully captured by her participation decision) offers several inherent advantages that facilitate the studying of whether over-participation in contests derives from the competitive nature of the contest setting or perhaps it is the product of a more general factor that can be found in non-competitive settings.…”