Sustaining cooperation in social exchange networks with incomplete global information

In this paper, we build a rating system that shapes the incentives of selfish users in such a way that they find it in their self-interest to cooperate with each other in social exchange networks. A rating system consists of a policy, which provides differential service for users with different ratings and a rating update rule, which rewards or penalizes users depending on whether they cooperate or not when they are asked to provide service. A key novelty of this paper is that we consider social exchange networks where users interact based on only incomplete global information about the rating distribution of the users participating in the network. We rigorously formalize the design problem of the optimal rating system which needs to be solved by the network designer as a coupled two-level optimization: users´ incentive problem and the efficiency maximization problem. We study the system dynamics of the social rating when users only have incomplete information. We prove that the users´ optimal decision problems exhibit threshold properties and hence, users need to have sufficient “trust” in the other network users to decide to cooperate. We also show how the optimal design depends on specific environment parameters (e.g. the benefit and cost of providing service in these networks) and which of these rating systems are sustainable when users are self-interested.