7 - Tortuous labyrinth: Noncooperative normal-form games between hyperrational players

Summary

It is characteristic of social interaction that I cannot maximize my own utility without “taking into account” (in some vague sense which we understand only darkly) what you are up to. I must have some theories or intuitions about how you are likely to behave, how you will respond to my actions, and the like. Worse than that, I must be aware that you are likely doing the same thing in regard to me, and I have to take that possibility into account as well. But of course you may know that I am aware of this possibility, and…adjust your behaviour accordingly. And so it goes – we are both involved in a tortuous labyrinth of relations.…

Moore and Anderson (1962, p. 413)

In this chapter I shall discuss noncooperative normal-form games between extremely rational (“hyperrational”) players. What is characteristic for such players is that they are supposed to maximize their expected utility on the basis of probability assignments that they somehow extract from the available nonprobabilistic information – from the common knowledge of the matrix of the game plus the assumptions of independence and rationality. In order to arrive at these probability assignments, the players are supposed to make use of the principle of insufficient reason.

I shall define the notion of a potential solution of such a hyperrational game: a so-called complete probabilistic equilibrium. It will turn out that some of the games of this kind lack a solution whereas others have more than one.