Asymptotic risk analysis for trust and reputation systems

Trust and reputation systems are decision support tools used to drive parties' interactions on the basis of parties' reputation. In such systems, parties rate with each other after each interaction. Reputation scores for each ratee are computed via reputation functions on the basis of collected ratings. We propose a general framework based on Bayesian decision theory for the assessment of such systems, with respect to the number of available ratings. Given a reputation function g and n independent ratings, one is interested in the value of the loss a user may incur by relying on the ratee's reputation as computed by the system. To this purpose, we study the behaviour of both Bayes and frequentist risk of reputation functions with respect to the number of available observations. We provide results that characterise the asymptotic behaviour of these two risks, describing their limits values and the exact exponential rate of convergence. One result of this analysis is that decision functions based on Maximum-Likelihood are asymptotically optimal. We also illustrate these results through a set of numerical simulations.