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Using strong isomorphisms to construct game strategy spaces

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  • Gagen, Michael

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.

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  • Gagen, Michael, 2012. "Using strong isomorphisms to construct game strategy spaces," MPRA Paper 40139, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:40139
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40, Elsevier.
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    More about this item

    Keywords

    non-cooperative games: isomorphic probability distributions: mixed strategy spaces;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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