Variational optimization of probability measure spaces resolves the chain store paradox

Michael Gagen () and Kae Nemoto

MPRA Paper from University Library of Munich, Germany

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.

Keywords: optimization; probability measure space; noncooperative game; chain store paradox (search for similar items in EconPapers)
JEL-codes: C02 C72 (search for similar items in EconPapers)
Date: 2006-05-11
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