Behavioral Mechanism Design: Optimal Contests 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 paper, 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 $V$ amongst 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 with homogenous participation costs $c_i = c$. Here, the optimal contest is always a simple contest, awarding equal prizes to the top $j^*$ contestants for a suitable choice of $j^*$. (In comparable models with strategic effort choices, 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 heterogeneous costs where agents' types are inherently two-dimensional, significantly complicating equilibrium analysis. 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.Comment: This is the full version of a paper in the ACM Conference on Economics and Computation (ACM-EC), 201

Optimal Crowdsourcing Contests

We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. Nonetheless, we show that crowdsourcing contests are 2-approximations to conventional methods for a large family of "regular" distributions, and 4-approximations, otherwise.Comment: The paper has 17 pages and 1 figure. It is to appear in the proceedings of ACM-SIAM Symposium on Discrete Algorithms 201

Contests for Status

We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A judicious definition of status categories can be used by a principal in order to influence the agents’ performance. We first consider a pure status case where there are no tangible prizes. Our main results connect the optimal partition in status categories to various properties of the distribution of ability among contestants. The top status category always contains an unique element. For distributions of abilities that have an increasing failure rate, a proliferation of status classes is optimal, while in other cases the optimal partition involves some coarseness. Finally, we modify the model to allow for status categories that are endogenously determined by monetary prizes of different sizes. If status is solely derived from monetary rewards, we show that the optimal partition in status classes contains only two categories

Information in tournaments under limited liability

The problem of designing tournament contracts under limited liability and alternative performance measures is considered. Under risk neutrality, only the best performing agent receives an extra premium if the liability constraint becomes binding. Under risk aversion, more than one prize is awarded. In both situations, performance measures can be ranked if their likelihood ratio distribution functions differ by a mean preserving spread. The latter result is applied to questions of contest design and more general forms of relative performance payment.contest, information, likelihood ratio distribution, tournament

Contests for Status

We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A judicious definition of status categories can be used by a principal in order to influence the agents’ performance. We first consider a pure status case where there are no tangible prizes. Our main results connect the optimal partition in status categories to various properties of the distribution of ability among contestants. The top status category always contains an unique element. For distributions of abilities that have an increasing failure rate, a proliferation of status classes is optimal, while in other cases the optimal partition involves some coarseness. Finally, we modify the model to allow for status categories that are endogenously determined by monetary prizes of different sizes. If status is solely derived from monetary rewards, we show that the optimal partition in status classes contains only two categories.

Knowing the gap - intermediate information in tournaments

Intermediate information is often available to competitors in dynamic tournaments. We develop two simple tournament models with two stages: one with intermediate information on subjects’ relative positions after the first stage, one without. In our models, equilibrium behavior in both stages is not changed by intermediate information. We test our formal analysis using data from laboratory experiments. We find no difference between average first and second stage efforts. With intermediate information, however, subjects adjust their effort to a higher extent. Subjects who lead tend to lower their second stage effort, subjects who lag still try to win the tournament. Overall, intermediate information does not endanger the effectiveness of rank-order tournaments: incentives do neither break down nor does a rat race arise. We also briefly investigate costly intermediate information

Continuois Time Contests

This paper introduces a contest model in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. Applications of the model include procurement contests and competitions for grants. We prove existence and uniqueness of the Nash equilibrium outcome, even if players have to choose bounded stopping times. We derive the equilibrium distribution in closed form. If the noise vanishes, the equilibrium outcome converges to - and thus selects - the symmetric equilibrium outcome of an all-pay auction. For two players and constant costs, each player’s profits increase if costs for both players increase, variance increases, or drift decreases. Intuitively, patience becomes a more important factor for contest success, which reduces informational rents

Concern for relative position, rank-order contests, and contributions to public goods

We study the consequences of concern for relative position and status in a public good economy. We consider a group of agents who are engaged in a contest for position whereby a set of rewards are distributed according to relative status. The extent of concern for rewards, together with the relative magnitude of rewards, will have an impact on agents’ willingness to contribute to public goods. Depending on the nature of prizes, i.e. whether higher private good consumption is rewarded or punished, the contest for relative position will either exacerbate or ameliorate the free-riding problem inherent in public good environments. In addition to examining the implications of concern for relative position, we also consider how an appropriate scheme of rewards might be designed to induce more efficient levels of public good.relative position; status seeking; public goods; contests