Abstract: I seek an understanding of the collective dynamics of systems of agents operating under an optimising dynamic. An autonomous agent has independent agency and decision-making capability. Placed in a system of such agents, however, the consequences of its actions, and hence its preferred choice of action (since it strives to behave optimally) are in°uenced and constrained by the activity of other agents. My work is divided into two complementary halves: the ¯rst examining the global consequences of local interactions; the second examines how the existence of global goals places requirements on the nature of those local interactions. Applications of the former lie primarily in the ¯eld of economic modelling; the latter in the ¯eld of distributed optimisation: (I) I propose a method for modelling economics systems in which outcomes depend locally on the predictions agents make of other agents. I investigate the circumstances under which coordination or coordination failure occurs in these predictive systems, and under which they will or will not evolve to (a) utilise all available information, (b) a rational expectations state. I analyse the observed punctuated equilibrium phenomena, and derive approximations to these complex economic systems, showing how qualitatively di®erent regimes of behaviour, and chaotic dynamics can naturally arise. (II) I present a new analysis of the NK search problem, demonstrating the existence of a sudden transition in problem di±culty. The theoretical predic- tions are compared with extensive empirical data from real problem instances. A novel stochastic optimisation algorithm is then introduced, derived from argu- ments motivated by the study of self-organised criticality in natural and arti¯cial systems. Its results and dynamics on several standard NP-complete problems are analysed. Comparisons are made with several of the standard optimisation heuristics used in computer science. I argue that emergent systems are those in which even perfect knowledge and understanding may give us no predictive information. In them the optimal means of prediction is simulation. I discuss the nature of boundedness and emergence in complex systems, arti¯cial intelligence and economics, and the ways in which simulation can help to develop rigorous scienti¯c theories. This thesis is motivated by the application of mathematical analysis to prob- lems which lie on the boundary of Applied Mathematics and the disciplines of Economics, Arti¯cial Intelligence and Computer Science, and so I also situate this work as best possible within the context of its relationships with these other ¯elds.

Abstract: Although agent-based models are not yet ready for practical investment application, they can yield powerful insights about market behavior, particularly in regard to the “second order” inefficiencies that create profit-making opportunities. When practical use of agent-based models becomes possible (perhaps within the next five years), their effectiveness will cause securities prices to change.

Abstract: In the course of this special topic, I decided with Dr. Patrick McSharry to analyze the stock market. My aim in this special topic is threefold: to analyze whether chaotic (deterministic) models can be applied to the stock market, explain why simple stochastic models do not reproduce the stock market entirely and lastly, present a relatively new method called agent based modelling.