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

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  • Marc Harper
  • Dashiell Fryer

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

Suggested Citation

  • Marc Harper & Dashiell Fryer, 2015. "Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex," Dynamic Games and Applications, Springer, vol. 5(3), pages 318-333, September.
    • Handle: RePEc:spr:dyngam:v:5:y:2015:i:3:p:318-333
    DOI: 10.1007/s13235-014-0124-0
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    Cited by:

    1. Hidekazu Yoshioka, 2024. "Generalized Logit Dynamics Based on Rational Logit Functions," Dynamic Games and Applications, Springer, vol. 14(5), pages 1333-1358, November.

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