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

作者：Harper Marc^*; Fryer Dashiell

来源：Dynamic Games and Applications, 2015, 5(3): 318-333.

DOI：10.1007/s13235-014-0124-0

• Evolutionary dynamics
• Evolutionary stability
• Lyapunov functions
• Riemannian geometry
• Time-scale calculus

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.

• 出版日期2015-9