As the number of online auction sites has increased, interest towards providing reliable summaries, reputations, about the past behaviour of sellers has risen. Existing approaches are often based on heuristics and hence proper evaluation of the systems is difficult. To improve the situation we introduce a game theoretical model for reputation in online auctions. As our second contribution we discuss how reputation systems can use Bayesian model averaging to integrate different information sources. We also discuss practical aspects and evaluate an experimental online reputation system that is based on the proposed framework. Our results indicate that mechanisms based on our framework increase the number of successful transactions significantly (in statistical sense) and result in mechanisms that are robust for changes in the behaviour of the participants.