Variational optimization of probability measure spaces resolves the chain store paradox

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dc.creatorGagen, Michael J.
dc.creatorNemoto, Kae
dc.date2006-04-27
dc.date2006-05-11
dc.date.accessioned2026-07-07T07:11:21Z
dc.date.available2026-07-07T07:11:21Z
dc.descriptionIn 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.
dc.description11 pages, 5 figures. Replaced for minor notational correction
dc.identifierhttps://arxiv.org/abs/math/0604611
dc.identifierhttp://arxiv.org/abs/math/0604611
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111722
dc.subjectOptimization and Control
dc.subjectStatistical Mechanics
dc.subjectComputer Science and Game Theory
dc.subject49J52; 49K27; 91A20
dc.titleVariational optimization of probability measure spaces resolves the chain store paradox
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