Gagen, Michael (2012): Using strong isomorphisms to construct game strategy spaces.
Download (249kB) | Preview
When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the dimensionality and volume of the underlying probability parameter spaces. These differences arise as probability theory employs structure preserving isomorphic mappings when constructing strategy spaces to analyze games. In contrast, game theory uses weaker mappings which change some of the properties of the underlying probability distributions within the mixed strategy space. In this paper, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games, and might resolve some of the paradoxes of game theory.
|Item Type:||MPRA Paper|
|Original Title:||Using strong isomorphisms to construct game strategy spaces|
|Keywords:||non-cooperative games: isomorphic probability distributions: mixed strategy spaces|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games|
|Depositing User:||Michael Gagen|
|Date Deposited:||21 Jul 2012 19:56|
|Last Modified:||16 Apr 2016 13:10|
J. von Neumann and O. Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, Princeton, 1944. Page numbers from 1953 edition.
J. F. Nash. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America, 36(1):48–49, 1950.
J. Nash. Non-cooperative games. Annals of Mathematics, 54(2):286–295, 1951.
H. W. Kuhn. Extensive games and the problem of information. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games, Volume II, Princeton Annals of Mathematical Studies, No. 28, Princeton, 1953. Princeton University Press.
S. Hart. Games in extensive and strategic forms. In R. J. Aumann and S. Hart, editors, Handbook of Game Theory with Economic Applications, pages 19–40, Amsterdam, 1992. North Holland.
R. Selten. A reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4:25–55, 1975.
D. Chatterjee. Abstract Algebra. Prentice-Hall, New Delhi, 2005.
K. Ito. Introduction to Probability Theory. Cambridge University Press, Cambridge, 1984.
R. M. Gray. Probability, Random Processes and Ergodic Processes. Springer, Dordrecht, 2009.
P. Walters. An Introduction to Ergodic Theory. Springer-Verlag, New York, 1982.
E. Sernesi. Linear Algebra: A Geometric Approach. Chapman and Hall, Boca Raton, 1993.
H.-O. Georgii. Stochastics: Introduction to Probability and Statistics. de Gruyter, Berlin, 2008.
J. Pinter. Global Optimization. From MathWorld–A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/GlobalOptimization.html.
F. P. Ramsey. A mathematical theory of savings. Economic Journal, 38(152):543–559, 1928.