Models of Growth Under Pressure

Abstract

The results of this chapter extend the results of Chapters 2 and 3 to the case of a countable state space of small players, and moreover, to the case of processes that allow for a change in the number of particles (thus going beyond the simple migrations that we have played with so far), where physical particles correspond in this setting to the coalitions (stable groups) of agents. This extension is carried out in order to include important models of evolutionary coalition-building, merging and splitting (banks, subsidiaries, etc.), strategically enhanced preferential attachment, and many others. The mathematics of this chapter is more demanding than in the rest of our presentation, and its results are not used in other parts of the book. It is based on some elements of infinite-dimensional analysis, the analysis of functions on the Banach space of sequences $l_1$ and of the ODEs in this space. We begin with brief description of the tools used.