Chapter on Psychological Game Theory
Book on Extensions of Epistemic Game Theory
My plan is to write a textbook on several extensions of Epistemic Game Theory:
1. Psychological games
2. Games with incomplete information
3. Games with unawareness
4. Games with non-expected utility
In each extension I will focus on the concept of "common belief in rationality": how it can be formalized, and how the resulting choices can be characterized by a recursive procedure.
Psychological Game Theory
I have now started writing the part on psychological games. In traditional game theory, the utility you derive from making a certain choice depends only on the belief you hold about the choices of your opponents. However, there are many natural situations where your utility may also explicitly depend on higher-order beliefs, such as the belief you hold about the belief your opponent holds about your own choice.
Think, for instance, of a situation where you wish to surprise your partner by the birthday gift you buy for him or her. In other words, your objective is to buy a gift such that you believe that your partner believes that you buy something else. In that case, the utility you derive from buying a certain gift depends explicitly on what you believe that your partner believes about the gift you buy.
Such situations cannot be modelled within tradional game theory, and hence call for a more general model where the utility of a player may depend on the belief he has about the belief his opponent has about his own choice, or perhaps even on the belief he has about the belief his opponent has about the belief he has about the opponent's choice, and so on.
Psychological game theory is a new, more general approach to game theory that enables us to model such situations. Within psychological game theory we can thus model psychological phenomena such as the wish to a surprise another person by the choice you make, or the wish to meet somebody's expectations, and other situations where the utility from making a certain choice depends on higher-order beliefs.
So, far I have completed a first draft of a first chapter, where I explain what a psychological game is, and how belief hierarchies can be encoded there. This chapter can be downloaded below.