On a Structure of the Set of Differential Games Values

Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)


The set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal payoff is obtained.


Differential Game Jacobi Equation Bellman Equation Minimax Solution Terminal Payoff 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton–Jacobi-Bellman equations. With appendices by Maurizio Falcone and Pierpaolo Soravia. Birkhauser Boston, Boston (1997)MATHCrossRefGoogle Scholar
  2. 2.
    Demyanov, V.F., Rubinov, A.M.: Foundations of Nonsmooth Analysis, and Quasidifferential Calculus. In Optimization and Operation Research 23, Nauka, Moscow (1990)Google Scholar
  3. 3.
    Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. CRC, Boca Raton (1992)MATHGoogle Scholar
  4. 4.
    Evans, L.C., Souganidis, P.E.: Differential games and representation formulas for solutions of Hamilton–Jacobi-Isaacs Equations. Indiana University Mathematical Journal 33, 773–797 (1984)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, New York (1988)MATHGoogle Scholar
  6. 6.
    McShane, E.J.: Extension of range of function. Bull. Amer. Math. Soc. 40, 837–842, (1934)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Subbotin, A.I.: Generalized solutions of first-order PDEs. The dynamical perspective. Birkhauser, Boston (1995)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and Mechanics UrB RASEkaterinburgRussia

Personalised recommendations