The search model of Diamond (1982) and its elaboration by Diamond and Fudenberg (1989) have been influential, as evidenced by frequent citations in the search literature. Diamond begins his analysis by assuming infinitely many agents in the model. Consequently, his dynamical analysis is entirely deterministic, and cycles of the model are generated by a set of deterministic differential equations. His model has no room for random fluctuations of the fraction of employed agents.

This is not to fault the model for lack of realism. Nevertheless, one would like to know how his model behaves in a finite-agent version: Does it produce substantial or negligible fluctuations about a locally stable state? Which of the multiple equilibria is chosen?

In this chapter, we recast their model in a framework of the modeling strategy advocated in this book. We have two objectives in recasting their model this way: One is to obtain information on fluctuations about the equilibria, and to provide a simpler explanation than Diamond and Fudenberg did for cyclical behavior. The other is to provide a new and more natural basis for equilibrium selection for models with multiple equilibria than those available in the economic literature on equilibrium selection.

By our reformulation a different view of cycles emerges. We will show that the model has multiple equilibria, and that stochastic fluctuations cause the fraction of the employed to move from one basin of attraction to another with positive probabilities.