Summary
Methods from the statistical mechanics of disordered systems are beginning to permeate game theory. If the game theoretical problem involves a large number of strategies and random payoff matrices, these methods may be efficiently used to determine the typical values of specific parameters characterizing the game and the corresponding optimal strategies. The present article gives a short pedagogical introduction to some of the relevant concepts of game theory and their relation to statistical mechanics, with a special emphasis on matrix and bimatrix games.
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.
Similar content being viewed by others
References
J. von Neumann, O. Morgenstern: Theory of Games and Economic Behaviour (Princeton Press, Princeton 1953 )
M. Mezard, G. Parisi, M.A. Virasoro: Spin Glass Theory and Beyond ( World Scientific, Singapore 1987 )
W. Kinzel, G. Reents: Physik per Computer ( Spektrum, Heidelberg 1996 )
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling: Numerical Recipes in C ( Cambridge University Press, Cambridge 1990 )
J. Berg, A. Engel: Phys. Rev. Lett. 81, 4999 (1998)
A. Engel, C. van den Broeck: Statistical Mechanics of Learning ( Cambridge University Press, Cambridge 2000 )
J.F. Nash. Annals of Mathematics 54, 268 (1951)
M. Szierzawa, M.-J. Oméro: http://xxx.lanl.gov/cond-mat/0007321
R. Axelrod, W.D. Hamilton: Science 211, 1390 (1981)
R. Axelrod: The Evolution of Cooperation ( Basic Books, New York 1984 )
Wang Jianhua: The Theory of Games ( Oxford University Press, Oxford 1988 )
J. Berg: Phys. Rev. E61, 2327 (2000), Statistical Mechanics of Random Games, PhD Thesis, Otto-von-Guericke-University, Magdeburg (1999)
J. Maynard Smith: Evolution and the Theory of Games ( Cambridge University Press, Cambridge 1993 )
J. Hofbauer, K. Sigmund: The Theory of Evolution and Dynamical Systems ( Cambrigde University Press, Cambridge 1988 )
S. Diederich, M. Opper: Phys. Rev. A39, 4333 (1989)
M. Opper, S. Diederich: Phys. Rev. Lett. 69, 1616 (1992)
W.B. Arthur: Am. Econ. Assoc. Papers and Proc. 84, 406 (1994)
http://www.unifr.ch/econophysics/minority/
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Engel, A. (2002). Game Theory and Statistical Mechanics. In: Computational Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04804-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-04804-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07571-1
Online ISBN: 978-3-662-04804-7
eBook Packages: Springer Book Archive