Here, we illustrate the notion of aggregate dynamics and fluctuations about locally stable equilibria using simple models, and in so doing introduce some important tools. We begin this chapter with a closed binary model with slightly more complex transition rates than the ones in Chapter 4. For this model we derive the dynamics of aggregate variables and fluctuations about the aggregate mean, both are derivable from the master equation.

Agents in this section still face binary choices, but no longer choose their decisions independently. Their choices are subject to externality. A simple way to incorporate interactions among the decision processes by agents in the model is to use nonlinear transition rates ln and rn. More specifically, we now assume that they depend on the fraction of agents with the same choice. This is a type of feedback effect of aggregate effects of the decisions by all the agents in the model.

The proposed reformulation illustrates a simple way of analyzing stochastic interaction patterns of a large number of microeconomic agents who are subject to aggregate effects, or field effects. These effects are distinguished from pairwise or neighborhood interactions among agents, patterned after the Ising model, or anonymous interaction patterns, often used in the literature on search. The kind of externalities discussed in this section is called social influence in Becker (1974, 1990) and is discussed in Akerlof (1980), and Akerlof and Milbourne (1980).