Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
Auyang, S.A.: Foundations of complex systems theories. Cambridge University Press, Cambridge (1998)
Di Gregorio, S., Serra, R., Villani, M.: Applying cellular automata to complex environmental problems: The simulation of the bioremediation of contaminated soils. Theoretical computer science 217, 131–156 (1999)
Farmer, J.D., Patelli, P., Zovko, I.I.: The Predicitive Power of Zero Intelligence in Financial Markets. PNAS USA 102, 2254–2259 (2005)
Fontana, W., Buss, L.W.: The arrival of the fittest: towards a theory of biological organization. Bull. Mathem. Biol. 56, 1–64 (1994)
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/0406058
Haken, H.: Synergetics: an introduction. Springer, Berlin (1983)
Holland, J.H., Holyoak, K.J., Nisbett, R.E., Thagard, P.R.: Induction. MIT Press, Cambridge (1986)
Jain, S., Krishna, S.: Autocatalytic sets and the growth of complexity in a simple model. Phys. Rev. Lett. 81, 5684–5687 (1998)
Jain, S., Krishna, S.: Emergence and growth of complex networks in adaptive systems. Computer Phys. Comm., 121–122, 116–121 (1999)
Lane, D., Maxfield, R.: Ontological uncertainty and innovation. Journal of Evolutionary Economics 15, 3–50 (2005)
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)
Lane, D., Serra, R., Villani, M., Ansaloni, L.: A theory based dynamical model of innovation processes. ComplexUs (in press, 2006)
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)
Nilsson, N.J.: Artificial Intelligence: a new synthesis. Morgan Kaufmann, San Francisco (1998)
Palmer, R.G., Arthur, B.W., Holland, J.J., LeBaron, B., Taylor, P.: Artificial economic life: A simple model of a stockmarket. Physica D 75, 264–274 (1994)
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)
Serra, R., Villani, M., Colacci, A.: Differential equations and cellular automata models of the growth of cell cultures and transformation foci. Complex Systems 13, 347–380 (2001)
Siegelmann, H.: Neural Networks and Analog Computation: Beyond the Turing Limit, Birkhäuser Boston, Basel, Berlin (1999)
Strogatz, S.H.: Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering. Perseus Books (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Serra, R., Villani, M. (2006). Agents, Equations and All That: On the Role of Agents in Understanding Complex Systems. In: Stock, O., Schaerf, M. (eds) Reasoning, Action and Interaction in AI Theories and Systems. Lecture Notes in Computer Science(), vol 4155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11829263_9
Download citation
DOI: https://doi.org/10.1007/11829263_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37901-0
Online ISBN: 978-3-540-37902-7
eBook Packages: Computer ScienceComputer Science (R0)