We introduce game theory as a formal framework in which exchange protocols can be modeled and their properties can be studied. We use this framework to give a formal definition for rational exchange relating it to the concept of Nash equilibrium in games. In addition, we study the relationship between rational exchange and fair exchange. We prove that fair exchange implies rational exchange, but the reverse is not true. The practical consequence of this is that rational exchange protocols may provide interesting solutions to the exchange problem by representing a trade-off between complexity and what they achieve. They could be particularly useful in mobile e-commerce applications.