| 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 influenced and constrained by the activity of other agents. My work is divided into two complementary halves: the first 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.; (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 evolve to (a) utilise all available information, (b) a rational expectations state. I analyse the observed punctuated equilibrium phenomena, and derive mathematical approximations to these complex economic systems, showing rigorously how qualitatively different 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 difficulty. The theoretical predictions are compared with extensive empirical data from real problem instances. A novel stochastic optimisation algorithm is then introduced, motivated by the phenomenon of self-organised criticality. Its results and dynamics on several standard NP-complete problems are analysed, and compared with several standard optimisation heuristics.; 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, artificial intelligence and economics.; This thesis is motivated by the application of mathematical analysis to problems which lie on the boundary of Applied Mathematics and the disciplines of Economics, Artificial Intelligence and Computer Science, and so I also situate this work as best possible within the context of its relationships with these other fields. |
