Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex

Marc Harper () and Dashiell Fryer ()

Dynamic Games and Applications, 2015, vol. 5, issue 3, 318-333

Abstract: We combine incentive, adaptive, and time-scale dynamics to study multipopulation dynamics on the simplex equipped with a large class of Riemannian metrics, simultaneously generalizing and extending many dynamics commonly studied in dynamic game theory and evolutionary dynamics. Each population has its own geometry, method of adaptation (incentive), and time-scale (discrete, continuous, and others). Using information-theoretic measures of distance we give a widely-applicable Lyapunov result for the dynamics. Copyright Springer Science+Business Media New York 2015

Keywords: Evolutionary dynamics; Evolutionary stability; Lyapunov functions; Riemannian geometry; Time-scale calculus (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13235-014-0124-0

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