Analytic solution for a class of linear quadratic open-loop Nash games

DOI10.1080/00207178608933518zbMath0593.90092OpenAlexW2070876577WikidataQ126245545 ScholiaQ126245545MaRDI QIDQ3724114

P. Bertrand, Hisham Abou-Kandil

Publication date: 1986

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207178608933518

zbMATH Keywords

analytic solutionopen-loop Nash strategyRiccati matrix differential equationslinear differential games with quadratic cost functionals

Mathematics Subject Classification ID

Game theory (91A99) Differential games (aspects of game theory) (91A23)

Related Items (21)

An algorithm for solving coupled differential matrix systems: Approximations, convergence and upper error bounds ⋮ Kronecker products and coupled matrix Riccati differential systems ⋮ Open-loop Nash equilibrium in polynomial differential games via state-dependent Riccati equation ⋮ On the open-loop Nash equilibrium in LQ-games ⋮ Magnus integrators for solving linear-quadratic differential games ⋮ Unnamed Item ⋮ Feedback strategies for discrete-time linear-quadratic two-player descriptor games ⋮ Algorithms for computing Nash equilibria in deterministic LQ games ⋮ Exact computable solution of a class of strongly coupled Riccati equations ⋮ Explicit solutions of Riccati equations appearing in differential games ⋮ Explicit solutions of Riccati equations appearing in differential games ⋮ A numerical toolbox to solve \(N\)-player affine LQ open-loop differential games ⋮ Generalized Riccati equations associated with guaranteed cost control: an overview of solutions and features ⋮ The open-loop linear quadratic differential game for index one descriptor systems ⋮ Computational aspects of the open-loop Nash equilibrium in linear quadratic games ⋮ Analytical solution for a class of linear quadratic open-loop Nash game with multiple players ⋮ Linear Quadratic Differential Games: An Overview ⋮ Asymptotic analysis of linear feedback Nash equilibria in nonzero-sum linear-quadratic differential games ⋮ Discrete-time Riccati equations in open-loop Nash and Stackelberg games. ⋮ Necessary conditions for constant solutions of coupled Riccati equations in Nash games ⋮ Exact solution of a class of strongly coupled Riccati matrix differential equations

Cites Work

• A series solution to the Nash strategy for large scale interconnected systems
• Nonzero-sum differential games
• Series Nash solution of two-person, nonzero-sum, linear-quadratic differential games
• On a class of nonzero-sum, linear-quadratic differential games
• On the solution of the open-loop Nash Riccati equations in linear quadratic differential games

This page was built for publication: Analytic solution for a class of linear quadratic open-loop Nash games