Reflexive analysis of groups

Abstract

This chapter develops further a model I previously introduced, of an agent facing a choice between the positive and the negative poles. Here I will consider agents whose individual behavior depends on a 'society' compounded by all of them. Four ideas underlie the theory. The first idea is to consider relationships between the subgroups of agents, not just pairs of agents; this idea allows us to represent a decomposable graph corresponding to an agent or a group of agents as a tree of subgraphs. The second idea is to establish a correspondence between decomposable graphs and polynomials, allowing us to replace a tree of subgraphs with a tree of polynomials representing a computational process. The third idea consists of the interpretation of the tree of polynomials as an agent who has images of the self, which can have images of the self, etc. Finally, the fourth idea is putting an equation into correspondence to the agent, allowing us to find out the agent's state. The theory is illustrated here with several examples from modern geopolitics, including scenarios of current interest. © 2009 Springer-Verlag Berlin Heidelberg.