Skip to main content

Stochastic Games and Nonexpansive Maps

  • Conference paper
Book cover Stochastic Games and Applications

Part of the book series: NATO Science Series ((ASIC,volume 570))

Abstract

This chapter studies asymptotic properties of the orbits of non-expansive maps defined on a normed space, and relates these properties to properties of the value of two-person zero-sum games and to properties of the minmax of n-person stochastic games.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann, R.J. and Maschler, M. (1995)Repeated Games with Incomplete InformationMIT Press, Cambridge.

    MATH  Google Scholar 

  2. Bewley, T. and Kohlberg, E. (1976) The asymptotic theory of stochastic gamesMathematics of Operations Research 1197–208.

    Article  MathSciNet  MATH  Google Scholar 

  3. Coulomb, J.-M. (2003) Games with a recursive structure, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 28, pp. 427–442.

    Google Scholar 

  4. Diestel, J. (1975)Geometry of Banach Spaces: Selected TopicsSpringer-Verlag, Berlin.

    MATH  Google Scholar 

  5. Forges, F. (1982) Infinitely repeated games of incomplete information: Symmetric case with random signalsInternational Journal of Game Theory11, 203–213.

    Article  MathSciNet  MATH  Google Scholar 

  6. Hoffmann-Jorgensen, J. and Pisier, G. (1976) The law of large numbers and the central limit theorem in Banach spacesAnnals of Probability4, 587–599.

    Article  MathSciNet  Google Scholar 

  7. Kohlberg, E. and Neyman, A. (1981) Asymptotic behavior of nonexpansive mapping in normed linear spacesIsrael Journal of Mathematics38, 269–275.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kohlberg, E. and Neyman, A. (1981) Asymptotic behavior of nonexpansive mappings in uniformly convex Banach spacesAmerican Mathematical Monthly88, 698–700.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kohlberg, E. and Neyman, A. (1999) A strong law of large numbers for nonexpansive vector-valued stochastic processesIsrael Journal of Mathematics111, 93–108.

    Article  MathSciNet  MATH  Google Scholar 

  10. Kohlberg, E. and Zamir, S. (1974) Repeated games of incomplete information: The symmetric caseAnnals of Statistics2, 1040–1041.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mertens, J.-F. and Neyman, A. (1981) Stochastic gamesInternational Journal of Game Theory 1053–66.

    Article  MathSciNet  MATH  Google Scholar 

  12. Mertens, J.-F., Sorin, S. and Zamir, S. (1994) Repeated games, CORE Discussion Papers 9420, 9421, 9422, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.

    Google Scholar 

  13. Mertens J.-F. and S. Zamir (1971) The value of two-person zero-sum repeated games with lack of information on both sidesInternational Journal of Game Theory 139–64.

    Article  MathSciNet  MATH  Google Scholar 

  14. Neyman, A. (2003) From Markov chains to stochastic games, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 2, pp. 9–25.

    Google Scholar 

  15. Neyman, A. (2003) Real algebraic tools in stochastic games, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 6, pp. 57–75.

    MathSciNet  Google Scholar 

  16. Neyman, A. (2003) Stochastic games: Existence of the minmax, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 11, pp. 173–193.

    MathSciNet  Google Scholar 

  17. Neyman, A. (1998) Nonexpansive maps and stochastic games, mimeo.

    Google Scholar 

  18. Neyman, A. and Sorin, S. (2001) Zero-sum two-person repeated games with public uncertain duration process, Discussion Paper 259, Center for the Study of Rationality, The Hebrew University of Jerusalem, Jerusalem, Israel.

    Google Scholar 

  19. Shapley, L.S. (1953) Stochastic gamesProceedings of the National Academy of Sciences of the U.S.A.39, 1095–1100 (Chapter 1 in this volume).

    Google Scholar 

  20. Sorin, S. (2003) Classification and basic tools, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 3, pp. 27–35.

    MathSciNet  Google Scholar 

  21. Sorin, S. (2003) Discounted stochastic games: The finite case, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 5, pp. 51–55.

    MathSciNet  Google Scholar 

  22. Sorin, S. (2003) Stochastic games with incomplete information, in A. Neyman and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 25, pp. 375–395.

    MathSciNet  Google Scholar 

  23. Sorin, S. (2003) The operator approach to zero-sum stochastic games, in A. Ney-man and S. Sorin (eds.)Stochastic Games and ApplicationsNATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Kluwer Academic Publishers, Dordrecht, Chapter 27, pp. 417–426.

    MathSciNet  Google Scholar 

  24. Woyczynski, W.A. (1975) Laws of large numbers for vector-valued martingalesBulletin de l’Académie Polonaise des Sciences23, 1199–1201.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media New York

About this paper

Cite this paper

Neyman, A. (2003). Stochastic Games and Nonexpansive Maps. In: Neyman, A., Sorin, S. (eds) Stochastic Games and Applications. NATO Science Series, vol 570. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0189-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0189-2_26

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1493-2

  • Online ISBN: 978-94-010-0189-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics