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Information exchange systems, such as BitTorrent, Yahoo Answers, Yelp, Amazon Mechanical Turk, differ in many ways, but all share a common vulnerability to selfish behavior and free-riding. In this paper, we build incentives schemes based on social norms. Social norms prescribe a social strategy for the agents in the system to follow and deploy reputation schemes to reward or penalize agents depending on whether they follow or deviate from the prescribed strategy when selecting actions. Because agents in these systems often have only limited capability to observe the global system information, e.g. the reputation distribution of the agents participating in the system, their beliefs about the reputation distribution are heterogeneous and biased. Such belief heterogeneity causes a positive fraction of agents to not follow the social strategy. In such practical scenarios, the standard equilibrium analysis deployed in the economics literature is no longer directly applicable and hence, the system design needs to consider these differences. To investigate how the system designs need to change, we focus on a simple social norm with binary reputation labels but allow adjusting the punishment severity through randomization. First, we model the belief heterogeneity using a suitable Bayesian belief function. Next, we formalize the agents' optimal decision problems and derive in which scenarios they follow the prescribed social strategy. Then we study how the system state is determined by the agents' strategic behavior. We are particularly interested in the robust equilibrium where the system state becomes invariant when all agents strategically optimize their decisions. By rigorously studying two specific cases where agents' belief distribution is constant or is linearly influenced by the true reputation distribution, we prove that the optimal reputation update rule is to choose the mildest possible punishment. This result is further confirmed for more sophisticated belie- influences in simulations. In conclusion, our proposed design framework enables the development of optimal social norms for various deployment scenarios with limited observations.