Statistical mechanics of reputation systems in autonomous networks

Reputation systems seek to infer which members of a community can be trusted based on ratings they issue about each other. We construct a Bayesian inference model and simulate approximate estimates using belief propagation (BP). The model is then mapped onto computing equilibrium properties of a spin glass in a random field and analyzed by employing the replica symmetric cavity approach. Having the fraction of positive ratings and the environment noise level as control parameters, we evaluate in different scenarios the robustness of the BP approximation and its theoretical performance in terms of estimation error. Regions of degraded performance are then explained by the convergence properties of the BP algorithm and by the emergence of a glassy phase. (AU)