Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games

We consider a noncooperative game in infinite time horizon, with linear dynamics and exponentially discounted quadratic costs. Assuming that the state space is one-dimensional, we prove that the Nash equilibrium solution in feedback form is stable under nonlinear perturbations. The analysis shows th...

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Bibliographic Details
Published inDynamic games and applications Vol. 8; no. 1; pp. 42 - 78
Main Authors Bressan, Alberto, Nguyen, Khai T.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2018
Springer Nature B.V
Subjects
Communications Engineering
Computer Systems Organization and Communication Networks
Differential games
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Feedback
Game Theory
Management Science
Mathematics
Mathematics and Statistics
Networks
Nonlinear analysis
Operations Research
Social and Behav. Sciences
Nash equilibrium
Noncooperative differential games
Infinite horizon
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Summary:We consider a noncooperative game in infinite time horizon, with linear dynamics and exponentially discounted quadratic costs. Assuming that the state space is one-dimensional, we prove that the Nash equilibrium solution in feedback form is stable under nonlinear perturbations. The analysis shows that, in a generic setting, the linear-quadratic game can have either one or infinitely many feedback equilibrium solutions. For each of these, a nearby solution of the perturbed nonlinear game can be constructed.
ISSN:2153-0785
2153-0793
DOI:10.1007/s13235-016-0206-2