Isomorphic Strategy Spaces in Game Theory
Michael Gagen (mjgagen@gmail.com)
MPRA Paper from University Library of Munich, Germany
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.
Keywords: non-cooperative game theory; isomorphic probability spaces (search for similar items in EconPapers)
JEL-codes: C02 C72 (search for similar items in EconPapers)
Date: 2013-04-10
New Economics Papers: this item is included in nep-gth and nep-hpe
References: Add references at CitEc
Citations:
Downloads: (external link)
https://mpra.ub.uni-muenchen.de/46176/1/MPRA_paper_46176.pdf original version (application/pdf)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:46176
Access Statistics for this paper
More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter (winter@lmu.de).