On the stability of the best reply map for noncooperative differential games

Alberto Bressan, Zipeng Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Consider a differential game for two players in infinite time horizon, with exponentially discounted costs. A pair of feedback controls (u * 1(x), u * 2(x))is Nash equilibrium solution if u * 1 is the best strategy for Player 1 in reply to u * 2, and u * 2 is the best strategy for Player 2, in reply to u * 1 . The aim of the present note is to investigate the stability of the best reply map: (u 1, 2→R 1(u 2)R 2(u 1)). For linear-quadratic games, we derive a condition which yields asymptotic stability, within the class of feedbacks which are affine functions of the state x ∈ ℝ n. An example shows that stability is lost, as soon as nonlinear perturbations are considered.

Original languageEnglish (US)
Pages (from-to)113-132
Number of pages20
JournalAnalysis and Applications
Volume10
Issue number2
DOIs
StatePublished - Apr 1 2012

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Non-cooperative Game
Differential Games
Affine Function
Nonlinear Perturbations
Equilibrium Solution
Asymptotic stability
Nash Equilibrium
Asymptotic Stability
Feedback Control
Feedback control
Horizon
Game
Feedback
Costs
Strategy
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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On the stability of the best reply map for noncooperative differential games. / Bressan, Alberto; Wang, Zipeng.

In: Analysis and Applications, Vol. 10, No. 2, 01.04.2012, p. 113-132.

Research output: Contribution to journalArticle

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