Agents, Equations and All That: On the Role of Agents in Understanding Complex Systems
Differential equations and agent-based models are different formalisms which can be applied to describe the evolution of complex systems. In this paper, it is shown how differential equations can describe interactions among agents: it is pointed out that their capabilities are broader than is often assumed, and it is argued that such an approach should be preferred whenever applicable. Also discussed are the circumstances in which it is necessary to resort to agent-based models, and a rigorous approach is advocated in these cases. In particular, the relationship between the model and a theory of the processes under consideration provides both stimuli and constraints for the model. This relationship is discussed both in general terms and with reference to a specific example, which concerns a model of innovation processes.
KeywordsCellular Automaton Innovation Process Information Processing Capability Zero Intelligence Evolve Complex System
Unable to display preview. Download preview PDF.
- 1.Arthur, B.W.: Out-of-Equilibrium Economics and Agent-Based Modeling. In: Judd, K.L.I., Tesfatsion, L. (eds.) Handbook of Computational Economics. Agent-Based Computational Economics, Amsterdam, North-Holland, vol. 2 (2005)Google Scholar
- 2.Arthur, B.W., Holland, J.J., LeBaron, B., Palmer, R., Taylor, P.: Asset pricing under endogenous expectations in an artificial stock market. In: Arthur, W.B., Durlauf, S., Lane, D. (eds.) Economy as an evolving complex system II (ch. 4), Redwood city (CA). Addison Wesley, Reading (1997)Google Scholar
- 3.Auyang, S.A.: Foundations of complex systems theories. Cambridge University Press, Cambridge (1998)Google Scholar
- 7.Görnerup, O., Crutchfield, J.P.: Objects That Make Objects: The Population Dynamics of Structural Complexity. Santa Fe Institute Working Paper 04-06-020, arxiv.org e-print adap-org/0406058Google Scholar
- 9.Holland, J.H., Holyoak, K.J., Nisbett, R.E., Thagard, P.R.: Induction. MIT Press, Cambridge (1986)Google Scholar
- 11.Jain, S., Krishna, S.: Emergence and growth of complex networks in adaptive systems. Computer Phys. Comm., 121–122, 116–121 (1999)Google Scholar
- 13.Lane, D., Serra, R., Villani, M., Ansaloni, L.: A theory based dynamical model of innovation processes. In: Bourgine, P., Kepes, F., Schoenauer, M. (eds.) Proceedings of the European Conference on Complex Systems ECCS 2005 (2005) (CD Rom: long paper #88)Google Scholar
- 14.Lane, D., Serra, R., Villani, M., Ansaloni, L.: A theory based dynamical model of innovation processes. ComplexUs (in press, 2006)Google Scholar
- 15.Maxfield, R., Lane, D.: Foresight, complexity and strategy. In: Arthur, W.B., Durlauf, S., Lane, D. (eds.) Economy as an evolving complex system II (ch. 4), Redwood city (CA). Addison-Wesley, Reading (1997)Google Scholar
- 18.Serra, R., Villani, M.: Exploring an agent-based model of innovation. In: Lane, D., Pumain, D., van der Leeuw, S., West, G. (eds.) Complexity perspectives on innovation and social change, Springer Methodos Series (in preparation, 2006)Google Scholar
- 20.Siegelmann, H.: Neural Networks and Analog Computation: Beyond the Turing Limit, Birkhäuser Boston, Basel, Berlin (1999)Google Scholar
- 21.Strogatz, S.H.: Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering. Perseus Books (1994)Google Scholar