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Variational optimization of probability measure spaces resolves the chain store paradox

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  • Gagen, Michael
  • Nemoto, Kae

Abstract

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.

Suggested Citation

  • Gagen, Michael & Nemoto, Kae, 2006. "Variational optimization of probability measure spaces resolves the chain store paradox," MPRA Paper 4778, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:4778
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    References listed on IDEAS

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    More about this item

    Keywords

    optimization; probability measure space; noncooperative game; chain store paradox;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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