Variable Temptations and Black Mark Reputations

In a world of imperfect information, reputations often guide the sequential decisions to trust and to reward trust. We consider two-player situations, where one player – the truster – decides whether to trust, and the other player – the temptee – has a temptation to betray when trusted. The strength of the temptation to betray varies from encounter to encounter. We refer to a recorded betrayal as a black mark and focus on mechanisms that only reveal the number of black marks of a temptee. We show that the greater the number of black marks, the less likely the temptee is to betray. We then study the different equilibria that emerge, depending on which side of the market has the ability to specify the equilibrium. In closing, we generalize to cases where the number of encounters is also recorded.