Evolutionary Game Theory: Why Equilibrium and Which Equilibrium

Two questions central to the foundations of game theory are (Samuelson 2002): (i) Why equilibrium? Should we expect Nash equilibrium play (players choosing best response strategies to the choices of others)? (ii) If so, which equilibrium? Which of the many Nash equilibria that arise in most games should we expect? To address the …rst question the classical game theory approach employs assumptions that agents are rational and they all have common knowledge of such rationality and beliefs. For a variety of reasons there has been wide dissatisfaction with such an approach. One major concern has to do with the plausibility and necessity of rationality and the common knowledge of rationality and beliefs. Are players fully rational, having unbounded computing ability and never making mistakes? Clearly, they are not. Moreover, the assumption of common (knowledge of) beliefs begs another question as to how players come to have common (knowledge of) beliefs. As we shall see in later discussion, under a very broad range of situations, a system may reach or converge to an equilibrium even when players are not fully rational (boundedly rational) and are not well-informed. As a result, it may be, as