Partial list of applications

A number of models, mostly elementary or simple, are presented in Chap­ters 4 through 11 to illustrate the methods and potential usefulness of the proposed approaches. Some more elaborate models are found in parts of Chapters 8 through 11, with some additional supporting material for them in Chapter 10.

One of the important consequences of our efforts is the derivation of aggre­gate, or emergent, or evolutionary patterns of behavior of large collections of agents. We deduce macroeconomic or sectoral properties or behavior of the microeconomic agents, starting from probabilistic descriptions of individ­ual agents. Thus, we go part way from the microeconomic specifications of models to macroeconomic models, a level of models called mesoscopic by van Kampen (1992). By mesoscopic, we mean that we can deduce (nearly) deter­ministic average behavior and associated fluctuations. For example, we may think of building sectoral models composed of a large number of firms as mesoscopic models. Several or many such mesoscopic models may then be connected, or aggregated, as macroeconomic models.

We examine with fresh and different views processes for diffusion of new ideas or practices among firms in an industry, due to innovation, changing eco­nomic and social environments, disturbances, or the appearance and spread of new products among firms of an industrial sector, such as new manufacturing processes, new inventions, new employment policies, and technical improve­ments. We also examine a well-known model in the search literature, due to Diamond (1982), from our finitary perspectives in Chapter 9. In taking a new look at the Diamond model, we show a new probabilistic equilibrium selec­tion criterion. In evaluating the Kiyotaki-Wright model (Kiyotaki and Wright 1993), which has similar dynamic structure to the Diamond model, we provide more dynamic analysis, and respecify their model so that money traders hold several units of money. Here, we show how partition vectors may be applied.

There are obviously many new results we can obtain in the area of indus­trial organization, such as entry and exit problems, changing market shares (Herfindahl index), or distributions of firm sizes or growth-rate distributions.

We also present, in Chapter 11, a simplified account of power laws that govern distributions of large price differences or returns in prices of some financial as­sets, and explanations of volatility switchings observed in financial time series, by examining conditions under which two large subgroups of agents with two opposing strategies form such that they largely determine the market excess demands for some financial assets.

1.3