Suppose when people interact with someone else, they have a choice between Good and Evil. Nobody directly observes the choice accurately, however. Instead, if someone chooses Evil it is observed with probability Y. The cost of being Good is G, but it results in a benefit of G+H to the other person in the interaction. The cost of being Evil is 0, but it results in a benefit of B < H to the other person. Thus, Good is efficient. Interactions are repeated an infinite number of times, with a discount rate of r and one interaction per period. Each person pays the other to interact with him. Thus, if I know you are Honest and are going to choose Good, I would pay you G+H, but I know you will choose Evil I will only pay you B.

It is common knowledge if somone is caught choosing Evil.

So far, this is rather like the Klein Leffler (1982) model of reputation. In one equilibrium, the Honest person has a reputation for Good to maintain, and so will be Good. In another equilibrium, the Honest person is mistrusted, and so will choose Evil.

But now let us add a different kind of Self-Fulfilling Distrust. Suppose that with probability Z, I come to believe you will choose Evil.

Actually, I will not finish this model. My hope was that I could build a neat model in which my use of a detection technology showed that I believed you would choose Evil. But it will not be as easy as I thought. I will post this anyway, though, as notes towards a start for a model.

I also wanted to note that this reasoning will not support a model of the tax system, because there, the interaction is not public. I would expect Self-Fulfilling Mistrust to arise in personal interactions, as in business contracts or marriage, but not in citizen-government contacts.