Feedback Nash equilibria for scalar N-player linear quadratic dynamic games
Benita Nortmann, Mario Sassano, Thulasi Mylvaganam
TL;DR
This paper introduces a graphical method to analyze feedback Nash equilibria in scalar N-player linear quadratic dynamic games, providing conditions for their existence and properties, supported by a numerical example.
Contribution
It presents a novel graphical representation for feedback Nash equilibria in scalar linear quadratic dynamic games, enabling easier analysis of equilibrium properties.
Findings
Derived conditions for the number of feedback Nash equilibria.
Provided a graphical tool for equilibrium analysis.
Illustrated results with a numerical example.
Abstract
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions for the number and properties of different feedback Nash equilibria a game may admit. The results are illustrated via a numerical example.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Optimization and Variational Analysis · Guidance and Control Systems