Incentives, gamification, and game theory: an economic approach to badge design

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, while others like Amazon and Y! Answers reward users for being amongst 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--- and 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 where winning a badge is valued and 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, and equilibrium participation and effort in an absolute standards mechanism Mα where badges are awarded for meeting some absolute level of (observed) effort, and a relative standards mechanism Mρ corresponding to competitive standards as in a top-\rs 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, Mα has zero-participation equilibria for standards that are too high, whereas all equilibria in Mρ elicit non-zero participation for all possible ρ, provided 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.