A fair exchange protocol is a protocol, in which two (or more) mutually suspicious parties exchange their digital items in a way that neither party can gain an advantage over the other by misbehaving. Many fair exchange protocols have been proposed in the academic literature, but they provide rather different types of fairness. The formal comparison of these proposals remained difficult, mainly, because of the lack of a common formal framework, in which each can be modelled and formal fairness definitions can be given. In this paper, we propose to use game theory for this purpose. We show how to represent fair exchange protocols with game trees and give three definitions of fairness using standard game theoretic notions. We are not aware of any other work that uses the apparatus of game theory for modelling fair exchange protocols.