Social Status and Badge Design

Many websites encourage user participation via the use of virtual rewards like badges. While badges typically have no explicit value, they act as symbols of social status within a community. In this paper, we study how to design virtual incentive mechanisms that maximize total contributions to a website when users are motivated by social status. We consider a game-theoretic model where users exert costly effort to make contributions and, in return, are awarded with badges. The value of a badge is determined endogenously by the number of users who earn an equal or higher badge; as more users earn a particular badge, the value of that badge diminishes for all users. We show that among all possible mechanisms for assigning status-driven rewards, the optimal mechanism is a leader-board with a cutoff: users that contribute less than a certain threshold receive nothing while the remaining are ranked by contribution. We next study the necessary features of ap-proximately optimal mechanisms and find that approximate optimality is influenced by the convexity of status valua-tions. When status valuations are concave, any approx-imately optimal mechanism must contain a coarse status partition, i.e. a partition of users into status classes whose size will grow as the population grows. Conversely when status valuations are convex, we prove that fine partition-ing, that is a partition of users into status classes whose size stays constant as the population grows, is necessary for approximate optimality