Characterization of Feedback Nash Equilibrium for Differential Games
Yurii Averboukh
TL;DR
This paper characterizes the set of Nash equilibrium payoffs in two-player differential games using nonsmooth analysis and provides conditions for continuous functions to form Nash equilibria, extending Hamilton-Jacobi methods.
Contribution
It introduces a novel characterization of Nash equilibrium payoffs in differential games via nonsmooth analysis and generalizes existing Hamilton-Jacobi approaches.
Findings
Characterization of Nash equilibrium payoffs using nonsmooth analysis.
Sufficient conditions for continuous functions to constitute Nash equilibria.
Extension of Hamilton-Jacobi methods to broader classes of differential games.
Abstract
We investigate the set of Nash equilibrium payoffs for two person differential games. The main result of the paper is the characterization of the set of Nash equilibrium payoffs in the terms of nonsmooth analysis. Also we obtain the sufficient conditions for a pair of continuous function to provide a Nash equilibrium. This result generalizes the method of system of Hamilton-Jacobi equations.
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Taxonomy
TopicsOptimization and Variational Analysis · Mathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Differential Equations Analysis