  Sustaining cooperation among self-interested agents is critical for the
proliferation of emerging online social communities, such as online communities
formed through social networking services. Providing incentives for cooperation
in social communities is particularly challenging because of their unique
features: a large population of anonymous agents interacting infrequently,
having asymmetric interests, and dynamically joining and leaving the community;
operation errors; and low-cost reputation whitewashing. In this paper, taking
these features into consideration, we propose a framework for the design and
analysis of a class of incentive schemes based on a social norm, which consists
of a reputation scheme and a social strategy. We first define the concept of a
sustainable social norm under which every agent has an incentive to follow the
social strategy given the reputation scheme. We then formulate the problem of
designing an optimal social norm, which selects a social norm that maximizes
overall social welfare among all sustainable social norms. Using the proposed
framework, we study the structure of optimal social norms and the impacts of
punishment lengths and whitewashing on optimal social norms. Our results show
that optimal social norms are capable of sustaining cooperation, with the
amount of cooperation varying depending on the community characteristics.
