Gagen, Michael and Nemoto, Kae (2006): Variational optimization of probability measure spaces resolves the chain store paradox.

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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.
Item Type:  MPRA Paper 

Institution:  University of Queensland 
Original Title:  Variational optimization of probability measure spaces resolves the chain store paradox 
Language:  English 
Keywords:  optimization; probability measure space; noncooperative game; chain store paradox 
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:  4778 
Depositing User:  Michael Gagen 
Date Deposited:  08 Sep 2007 
Last Modified:  28 Sep 2019 15:22 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/4778 