Gagen, Michael (2012): Using strong isomorphisms to construct game strategy spaces.

PDF
MPRA_paper_40139.pdf Download (249kB)  Preview 
Abstract
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 
Language:  English 
Keywords:  noncooperative games: isomorphic probability distributions: mixed strategy spaces 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  40139 
Depositing User:  Michael Gagen 
Date Deposited:  21 Jul 2012 19:56 
Last Modified:  15 Jun 2017 14:58 
References:  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 nperson games. Proceedings of the National Academy of Sciences of the United States of America, 36(1):48–49, 1950. J. Nash. Noncooperative 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. PrenticeHall, 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. SpringerVerlag, 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. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40139 