Gamification is growing increasingly prevalent as a means to incentivize user engagement of social media sites that rely on user contributions. Badges, or equivalent rewards, such as top-contributor lists that are used to recognize a user's contributions on a site, clearly appear to be valued by users who actively pursue and compete for them. However, different sites use different badge designs, varying how, and for what, badges are awarded. Some sites, such as StackOverflow, award badges for meeting fixed levels of contribution. Other sites, such as Amazon and Y! Answers, reward users for being among some top set of contributors on the site, corresponding to a competitive standard of performance. Given that users value badges, and that contributing to a site requires effort, how badges are designed will affect the incentives-therefore the participation and effort-elicited from strategic users on a site.We take a game-theoretic approach to badge design, analyzing the incentives created by widely used badge designs in a model in which winning a badge is valued, effort is costly, and potential contributors to the site endogenously decide whether or not to participate, and how much total effort to put into their contributions to the site. We analyze equilibrium existence, as well as equilibrium participation and effort, in an absolute standards mechanism M α in which badges are awarded for meeting some absolute level of (observed) effort, and a relative standards mechanism M ρ corresponding to competitive standards, as in a top-ρ contributor badge. We find that equilibria always exist in both mechanisms, even when the value from winning a badge depends endogenously on the number of other winners. However, M α has zero-participation equilibria for standards that are too high, whereas all equilibria in M ρ elicit nonzero participation for all possible ρ, provided that ρ is specified as a fixed number rather than as a fraction of actual contributors (note that the two are not equivalent in a setting with endogenous participation). Finally, we ask whether or not a site should explicitly announce the number of users winning a badge. The answer to this question is determined by the curvature of the value of winning the badge as a function of the number of other winners.

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.