2012/08/20 by Michael J. Gagen, M. J. Gagen, Gagen, Michael J.
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · Social Sciences · #Computer Science and Game Theory (cs.GT) #Computer science #Curse of dimensionality #Data Analysis #Entropy (arrow of time) #Evolutionary Game Theory and Cooperation #Example of a game without a value #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Game Theory and Applications #Game theory #Mathematical economics #Mathematics #Normal-form game #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Repeated game #Statistics #Statistics and Probability (physics.data-an) #Strategy #cs.GT #math.OC #physics.data-an
paper · pdf · doi:10.48550/arxiv.1208.3976
published in Munich Personal RePEc Archive (Ludwig Maximilian University of Munich) (Ludwig-Maximilians-Universität München) · 14 pages, 6 figures
arxiv created 2012/08/20 · openalex publication_date 2012/08/20 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the dimensionality and volume of the underlying probability parameter spaces. These differences arise as probability theory employs structure preserving isomorphic mappings when constructing strategy spaces to analyze games. In contrast, game theory uses weaker mappings which change some of the properties of the underlying probability distributions within the mixed strategy space. In this paper, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games, and might resolve some of the paradoxes of game theory.