Towards a Theory of Autonomous, Optimising Agents

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. Applications of the former lie primarily in the field of economic modelling; the latter in the field 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 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, derived from arguments motivated by the study of self-organised criticality in natural and artificial 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, artificial intelligence and economics, and the ways in which simulation can help to develop rigorous scientific theories. 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. To Stuart Kauffman who has been an excellent mentor and friend, without whom I’m sure I would have pursued a quite different line of research. To Eric Maskin for his persistent advice, criticism, clear-thinking and rigorous standards without whom this dissertation would have been a much inferior piece of work. To Harvard University and in particular to the remainder of my committee: Yu-Chi Ho, Tony Oettinger and Maja Matarić for supporting research which didn’t fit into the existing departments. To the Santa Fe Institute for introducing me to complex systems at their excellent summer school and supporting me during numerous research visits, and to Bios Group for their flexibility which helped me to complete my research in a reasonably timely fashion. Finally to my family and friends for their ever-present interest and support.