2006/04/27 by Michael J. Gagen, M. J. Gagen, Kae Nemoto +2
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · Social Sciences · #49J52 #49K27 #91A20 #Complex Systems and Time Series Analysis #Computer Science and Game Theory (cs.GT) #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Game Theory and Applications #Optimization and Control (math.OC) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #cs.GT #math.OC #msc:49J52 #msc:49K27 #msc:91A20
paper · pdf · doi:10.48550/arxiv.math/0604611
11 pages, 5 figures. Replaced for minor notational correction
openalex publication_date 2006/04/27 · arxiv created 2006/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.