Game theory for wireless networking: Is a Nash equilibrium always a desirable solution?

During the last decade there has been a great interest in applying game theory to several problems of wireless networking. The main focus of the existing research so far has been to ensure and prove that the game shall eventually reach a Nash equilibrium solution. In this paper our aim is to question whether a Nash equilibrium must be used as an allpurpose treatment without taking into consideration additional factors. Specifically, by exploiting the concept of equilibrium phase transitions from statistical mechanics we argue that in the case of a dynamic wireless environment - where the system might be constantly drifting from the Nash equilibrium due to external factors - the Nash equilibrium might be a particularly unstable outcome in terms of the overall performance and hence not a desirable outcome.