Honest behavior that reveals nothing about disposition leaves a trader’s reputation unchanged.

Evidence

Using techniques developed in the important work of Kreps and Wilson (1982) on games of incomplete information, we can show that such reasoning on the part of participants is mutually consistent if T is large. I shall not go into technicalities. But it can be shown that if Tis large there is a set of credible strategies, one per participant, where for a large number of initial periods customers come to the showroom, one by one, and where the salesman sells a reliable car (i.e. chooses B) irrespective of his true disposition, thus maintaining his reputation at the initial estimate p. (The reason the estimate does not change is that behaviour in these periods is independent of the salesman’s disposition, that is, independent of whether he is honest or dishonest. This being so, the fact that he sells reliable cars provides no information about his true disposition. Hence his reputation does not change.) — Diego Gambetta, Trust - Making and Breaking Cooperative…, 990

Categorization

• DEFINE: The key mechanism: reputation only updates when behavior is disposition-dependent. A dishonest seller mimicking honest behavior keeps his estimated reputation pinned at the prior p precisely because his choice carries no information.
• DEEPTHINKING: The insight that perfect mimicry erases information about the underlying type is a genuinely subtle epistemic point — noise-free pretending reveals nothing, so a rational observer’s assessment is frozen. This is a rich, sit-with-it result about signal value.