Strategic Learning and Robust Protocol Design for Online Communities   with Selfish Users
  This paper focuses on analyzing the free-riding behavior of self-interested users in online communities. Hence, traditional optimization methods for communities composed of compliant users such as network utility maximization cannot be applied here. In our prior work, we show how social reciprocation protocols can be designed in online communities which have populations consisting of a continuum of users and are stationary under stochastic permutations. Under these assumptions, we are able to prove that users voluntarily comply with the pre-determined social norms and cooperate with other users in the community by providing their services. In this paper, we generalize the study by analyzing the interactions of self-interested users in online communities with finite populations and are not stationary. To optimize their long-term performance based on their knowledge, users adapt their strategies to play their best response by solving individual stochastic control problems. The best-response dynamic introduces a stochastic dynamic process in the community, in which the strategies of users evolve over time. We then investigate the long-term evolution of a community, and prove that the community will converge to stochastically stable equilibria which are stable against stochastic permutations. Understanding the evolution of a community provides protocol designers with guidelines for designing social norms in which no user has incentives to adapt its strategy and deviate from the prescribed protocol, thereby ensuring that the adopted protocol will enable the community to achieve the optimal social welfare. 
Yu Zhang, Mihaela van der Schaar
cs.LG cs.GT cs.SI