Group structure and collective behavior

Abstract

The present dissertation consists of four chapters, which are loosely connected by the abstract relation between group structure and collective behavior. Three main abstractions of group structure are proposed, viz. time-dependent group which can be characterized by dynamical system, preference-dependent group that depends on aggregation of individual preferences, and relation-dependent group which is known as network.

In this respect, some interesting problems are investigated so as to demonstrate the effects of group structure on collective behavior. In detail, Chapter 1 studies such properties as dynamics, chaos, and stability in a typical time-dependent group, which also lays some solid foundations for the studies in the other three chapters. Chapter 2 investigates separable and additive aggregation rules in a preference-dependent group, with the aim of developing algebraic-geometric principles to efficiently identify additive aggregation rules. In particular, the Thomsen condition has been revisited and shown to be a both sufficient and necessary requirement for an aggregation rule being additive on a quite general two-dimensional domain.

Chapter 3 can be thought of as an application of time-dependent group in equity markets, in which quotation formation and dynamics are discussed in great detail. Some significant assertions on stability and stochastic stability are developed by means of market conditions. Chapter 4 relies on collective decision-making process on a government network to show how decisions are contingent on different network structures, which can be classified as H-form government line, M-form government star, and more general mixed-form network.