Gagen, Michael (2013): Isomorphic Strategy Spaces in Game Theory.

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Abstract
This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same strategic situation. In particular, 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. Here, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games . Specific example games considered are the chain store paradox, the trust game, the ultimatum game, the public goods game, the centipede game, and the iterated prisoner's dilemma. In general, our approach provides rational outcomes which are consistent with observed human play and might thereby resolve some of the paradoxes of game theory.
Item Type:  MPRA Paper 

Original Title:  Isomorphic Strategy Spaces in Game Theory 
Language:  English 
Keywords:  noncooperative game theory, isomorphic probability spaces 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  46176 
Depositing User:  Michael Gagen 
Date Deposited:  14 Apr 2013 07:00 
Last Modified:  05 Oct 2019 13:58 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/46176 