Skip to main content
SpringerLink
Log in
Book cover

Advances in Dynamic Games pp 3–23Cite as

On a Structure of the Set of Differential Games Values

  • Chapter
  • First Online:

  • 1457 Accesses

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

Abstract

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.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Book  MATH  Google Scholar 

  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. Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. CRC, Boca Raton (1992)

    MATH  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, New York (1988)

    MATH  Google Scholar 

  6. McShane, E.J.: Extension of range of function. Bull. Amer. Math. Soc. 40, 837–842, (1934)

    Article  MathSciNet  Google Scholar 

  7. Subbotin, A.I.: Generalized solutions of first-order PDEs. The dynamical perspective. Birkhauser, Boston (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics UrB RAS, S. Kovalevskaya street 16, GSP-384, 620219, Ekaterinburg, Russia

    Yurii Averboukh

Authors
  1. Yurii Averboukh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yurii Averboukh .

Editor information

Editors and Affiliations

  1. , HEC Montréal, Department of Management Science, 3000 Chemin de la Côte-Sainte-Catherine, Montreal, H3T2A7, Canada

    Michèle Breton

  2. Wrocław University of Technology, Institute of Mathematics and Computer Sc, Wybrzeże Wyspiańskiego 27, Wrocław, PL-50-370, Poland

    Krzysztof Szajowski

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Averboukh, Y. (2011). On a Structure of the Set of Differential Games Values. In: Breton, M., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 11. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8089-3_1

Download citation

Publish with us

Policies and ethics

Search

Navigation