Abstract
The Nash Equilibrium is a much discussed, deceptively complex, method for the analysis of non-cooperative games (McLennan and Berg, 2005). If one reads many of the commonly available definitions the description of the Nash Equilibrium is deceptively simple in appearance. Modern research has discovered a number of new and important complex properties of the Nash Equilibrium, some of which remain as contemporary conundrums of extraordinary difficulty and complexity (Quint and Shubik, 1997). Among the recently discovered features which the Nash Equilibrium exhibits under various conditions are heteroclinic Hamiltonian dynamics, a very complex asymptotic structure in the context of two-player bi-matrix games and a number of computationally complex or computationally intractable features in other settings (Sato, Akiyama and Farmer, 2002). This paper reviews those findings and then suggests how they may inform various market prediction strategies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Arthur, W. Brian “Inductive Reasoning and Bounded Rationality”, American Economic Review, (Papers and Proceedings), 84,406–411, 1994.
Epstein, Joshua M, and Hammond, Ross A “Non-Explanatory Equilibria: An Extremely Simple Game with (Mostly) Unattainable Fixed Points.” in Complexity, Vol.7, No. 4: 18–22,2002
Gul, F., Pearce, D., and Stachhetti, E. (1993) “A Bound on the Proportion of Pure Strategy Equilibria in Generic Games” Mathematics of Operations Research, Vol. 18, No. 3 (Aug., 1993), pp. 548–552
Lemke. CE. and Howson, J.T. (1964) “Equilibrium points of bimatrix games”, Journal of the Society for Industrial and Applied Mathematics, 12:413–423, 1964.
McLennan, Andrew & Berg, Johannes, 2005. “Asymptotic expected number of Nash equilibria of two-player normal form games,” Games and Economic Behavior, Elsevier, vol. 51(2), pages 264–295, May.
McLennan, A and Park, I (1999) “Generic 4×4 Two Person Games Have at Most 15 Nash Equilibria”, Games and Economic Behavior, 26–1, (January, 1999), 111—130.
Nash, John (1950) Non-Cooperative Games, Doctoral Dissertation, Faculty of Mathematics, Princeton University, 1950
Quint, Thomas and Shubik, Martin, (1997) “A Bound on the Number of Nash Equilibria in a coordination game”, Cowles Foundation Discussion Paper 1095, Yale University, 1997. http://cowles.econ.yale.edu/P/cd/dl0b/dl095.pdf
Sato, Y., Akiyama, E. and Farmer, J.D. (2001) “Chaos in Learning a Simple Two Person Game”, Santa Fe Institute Working Papers, 01-09-049. Subsequently published in Proceedings of the National Academy of. Sciences,. USA, 99, pp. 4748–4751, (2002).
Sandholm, T., Gilpin, A., & Conitzer, V. (2005). Mixed-integer programming methods for finding Nash equilibria. Proceedings of the National Conference on Artificial Intelligence (AAAI) (pp. 495–501). Pittsburgh, PA, USA.
von Stengel, Bernhard (1997) “New lower bounds for the number of equilibria in bimatrix games” Technical Report 264, Dept. of Computer Science, ETH Zurich, 1997.
von Stengel, Bernhard (2000) “Improved equilibrium computation for extensive two-person games”, First World Congress of the Game Theory Society (Games 2000), July 24–28, 2000 Basque Country University and Fundacion B.B.V., Bilbao, Spain.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fellman, P.V. (2011). The Nash Equilibrium Revisited: Chaos and Complexity Hidden in Simplicity. In: Minai, A.A., Braha, D., Bar-Yam, Y. (eds) Unifying Themes in Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17635-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-17635-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17634-0
Online ISBN: 978-3-642-17635-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)