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

Alberto Bressan, Zipeng Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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