Abstract
Since von Neumann and Morgenstern initiated the field of game theory,1 it has often proved of great value for the quantitative description and understanding of competition and co-operation between individuals. Game theory focusses on two questions: 1. Which is the optimal strategy in a given situation? 2. What is the dynamics of strategy choices in cases of repeatedly interacting individuals? In this connection game dynamical equations2 find a steadily increasing interest. Although they agree with the replicator equations of evolution theory (cf. Sec. II), they cannot be justified in the same way. Therefore, we will be looking for a foundation of the game dynamical equations which is based on individual actions and decisions (cf. Sec. IV).
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
J. von Neumann/O. Morgenstern, Theory of Games and Economic Behavior. Princeton: Princeton University Press 1944.
P. Taylor/L. Jonker, “Evolutionarily Stable Strategies and Game Dynamics”, in: Math. Biosciences, 40, 1978, pp.145–156; J. Hofbauer and K. Sigmund, Evolutionstheorie und dynamische Systeme. Berlin: Parey 1984.
W. Schnabl/P.F. Stadler/C. Forst/P. Schuster, “Full Characterization of a Strange Attractor. Chaotic Dynamics in Low-Dimensional Replicator Systems”, in: Physica D, 48, 1991, pp. 65–90.
W. Weidlich/G. Haag, Concepts and Models of a Quantitative Sociology. The Dynamics of Interacting Populations. Berlin: Springer, 1983.
K. H. Schlag, “Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits”, Discussion Paper No. B-361, Department of Economics, University of Bonn.
D. Helbing, “Interrelations between Stochastic Equations for Systems with Pair Interactions”, in: Physica A, 181, 1992, pp.29–52.
W. B. Arthur, “Competing Technologies, Increasing Returns, and Lock-In by Historical Events”, in: The Economic Journal 99, 1989, pp. 116–131.
For illustrative reasons, a small number of individuals (N = 40) and a broad initial probability distribution have been chosen. In each picture, the box is twice as high as the maximal occuring value of the probability.
D. Helbing, `A Stochastic Behavioral Model and a `Microscopic’ Foundation of Evolutionary Game Theory“, in: Theory and Decision 40, 1996, pp. 149–179.
N. S. Glance and B. A. Huberman, “Dynamics with Expectations”, in: Physics Letters A 165, 1992, pp. 432–440.
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems. Cambridge: Cambridge University Press 1988.
D. Helbing, Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes. Dordrecht: Kluwer Academic 1995.
D. Helbing, Stochastische Methoden, nichtlineare Dynamik und quantitative Modelle sozialer Prozesse, 2nd edition. Aachen: Shaker 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Helbing, D. (1998). Microscopic Foundation of Stochastic Game Dynamical Equations. In: Leinfellner, W., Köhler, E. (eds) Game Theory, Experience, Rationality. Vienna Circle Institute Yearbook [1997], vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1654-3_18
Download citation
DOI: https://doi.org/10.1007/978-94-017-1654-3_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4992-6
Online ISBN: 978-94-017-1654-3
eBook Packages: Springer Book Archive