On the existence of Nash strategies and solutions to coupled Riccati equations in linear-quadratic games

DOI10.1007/BF00933600zbMath0424.90095MaRDI QIDQ1135220

Cruz, J. B. jun., George P. Papavassilopoulos, J. V. Medanić

Publication date: 1979

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

stabilitylinear-quadratic gamesweighting matricesBrouwer's fixed-point theoremdegree of stabilitycoupled Riccati equationsexistence of Nash strategiesinfinite period of timelinear closed-loop Nash strategies

Mathematics Subject Classification ID

Differential games (aspects of game theory) (91A23) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (16)

Properties of feedback Nash equilibria in scalar LQ differential games ⋮ Recursive solution of linear-quadratic Nash games for weakly interconnected systems ⋮ Necessary and sufficient conditions for feedback Nash equilibria for the affine-quadratic differential game ⋮ Characterization of feedback Nash equilibria for multi-channel systems via a set of non-fragile stabilizing state-feedback solutions and dissipativity inequalities ⋮ University-students game ⋮ Learning feedback Nash strategies for nonlinear port-Hamiltonian systems ⋮ An iterative computational scheme for solving the coupled Hamilton-Jacobi-Isaacs equations in nonzero-sum differential games of affine nonlinear systems ⋮ Feedback Nash equilibria for linear quadratic descriptor differential games ⋮ A numerical algorithm to calculate the unique feedback Nash equilibrium in a large scalar LQ differential game ⋮ On the selection of one feedback Nash equilibrium in discounted linear-quadratic games ⋮ Algorithms for computing Nash equilibria in deterministic LQ games ⋮ Infinite horizon noncooperative differential games ⋮ Sufficient conditions for Stackelberg and Nash strategies with memory ⋮ A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games ⋮ Asymptotic analysis of linear feedback Nash equilibria in nonzero-sum linear-quadratic differential games ⋮ Time Consistency, Subgame Perfectness, Solution Concepts and Information Patterns in Dynamic Models of Stabilization Policies

Cites Work

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• A new approach to \(n\)-person, nonzero sum, linear differential games
• Counterexample in linear-quadratic games: Existence of nonlinear Nash solutions
• Nonzero-sum differential games
• On a class of nonzero-sum, linear-quadratic differential games
• Values and strategies for infinite time linear quadratic games
• On values and strategies for infinite-time linear quadratic games
• Existence and Uniqueness of Equilibrium Points for Concave N-Person Games
• N-Person Nonzero Sum Differential Games with Linear Dynamics

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