• DocumentCode
    1425959
  • Title

    The solution set of the N-player scalar feedback Nash algebraic Riccati equations

  • Author

    Engwerda, J.C.

  • Author_Institution
    Dept. of Econometrics, Tilburg Univ., Netherlands
  • Volume
    45
  • Issue
    12
  • fYear
    2000
  • fDate
    12/1/2000 12:00:00 AM
  • Firstpage
    2363
  • Lastpage
    2368
  • Abstract
    We analyze the set of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar N-player linear-quadratic differential game. We show that in general there exist at most 2N-1 solutions of the ARE that give rise to a Nash equilibrium. In particular we analyze the number of equilibria as a function of the autonomous growth parameter and present both necessary and sufficient conditions for the existence of a unique solution of the ARE
  • Keywords
    Riccati equations; differential equations; differential games; feedback; linear quadratic control; N-player scalar feedback Nash algebraic Riccati equations; autonomous growth parameter; feedback Nash equilibria; necessary conditions; scalar N-player linear-quadratic differential game; sufficient conditions; Control systems; Differential algebraic equations; Differential equations; Econometrics; Environmental economics; Game theory; Linear feedback control systems; Nash equilibrium; Riccati equations; Sufficient conditions;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/9.895575
  • Filename
    895575
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1425959