Introduction

In the last two chapters we have explored the nature of classic rationalexpectations equilibria and the kinds of circumstances in which such equilibria could possibly arise. As we have seen, the idea of an equilibrium characterized by agents acting according to mathematical expectations is at its most convincing in a world of many agents, each with an individually insignificant impact upon the outcome. To date, however, we have not explored a further question that has a bearing on the existence problem: From some initial starting point that may not be an equilibrium state, can the system find its way to a rational-expectations equilibrium? From the game-theoretic point of view this is the problem of solution by real-time (rather than, say, fictitious) play. In the economics literature, it is often referred to as a learning problem. For reasons to be outlined shortly, it is doubtful whether this usage is capable of representing the full complexity of the problem. However, if we agree to adopt a somewhat teleological viewpoint and ascribe learning to the system as a whole rather than to the individuals whose behavior drives the system, the usage refers to the way in which the system as a whole gropes its way toward a full rational-expectations equilibrium, in which every individual participant is in his or her personal state of rational expectations conditional upon the individual information sets. Of course, this assumes that the system is capable of doing this.