Existence and Uniqueness of Disturbed Open-Loop Nash Equilibria for Affine-Quadratic Differential Games

  • Teresa-Paula Azevedo-Perdicoúlis
  • Gerhard Jank
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)


In this note, we investigate the solution of a disturbed quadratic open loop (OL) Nash game, whose underlying system is an affine differential equation and with a finite time horizon. We derive necessary and sufficient conditions for the existence/uniqueness of the Nash/worst-case equilibrium. The solution is obtained either via solving initial/terminal value problems (IVP/TVP, respectively) in terms of Riccati differential equations or solving an associated boundary value problem (BVP). The motivation for studying the case of the affine dynamics comes from practical applications, namely the optimization of gas networks. As an illustration, we applied the results obtained to a scalar problem and compare the numerical effectiveness between the proposed approach and an usual Scilab BVP solver.


Nash Equilibrium Boundary Value Problem Open Loop Differential Game Dynamic Game 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Teresa-Paula Azevedo-Perdicoúlis
    • 1
  • Gerhard Jank
    • 2
  1. 1.ISR-pólo de Coimbra & Departamento MatemáticaUTADVila RealPortugal
  2. 2.Universidade de AveiroAveiroPortugal

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