  We consider a distributed multi-user system where individual entities possess
observations or perceptions of one another, while the truth is only known to
themselves, and they might have an interest in withholding or distorting the
truth. We ask the question whether it is possible for the system as a whole to
arrive at the correct perceptions or assessment of all users, referred to as
their reputation, by encouraging or incentivizing the users to participate in a
collective effort without violating private information and self-interest. Two
specific applications, online shopping and network reputation, are provided to
motivate our study and interpret the results. In this paper we investigate this
problem using a mechanism design theoretic approach. We introduce a number of
utility models representing users' strategic behavior, each consisting of one
or both of a truth element and an image element, reflecting the user's desire
to obtain an accurate view of the other and an inflated image of itself. For
each model, we either design a mechanism that achieves the optimal performance
(solution to the corresponding centralized problem), or present individually
rational sub-optimal solutions. In the latter case, we demonstrate that even
when the centralized solution is not achievable, by using a simple
punish-reward mechanism, not only a user has the incentive to participate and
provide information, but also that this information can improve the system
performance.

Computer Science and Game Theory