Skip to main content
SpringerLink
Log in
Book cover

Advances in Dynamic Games and Applications pp 257–266Cite as

Birkhäuser

A Game Variant of the Stopping Problem on Jump Processes with a Monotone Rule

  • Conference paper

  • 532 Accesses

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 5))

Abstract

A continuous-time version of the multivariate stopping problem is considered. Associated with vector-valued jump stochastic processes, stopping problems with a monotone logical rule are defined under the notion of the Nash equilibrium point. The existence of an equilibrium strategy and its characterization by integral equations are obtained. Illustrative examples are provided.

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   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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellman, R. Stability Theory of Differential Equations. McGraw-Hill, New York, 1953.

    MATH  Google Scholar 

  2. Feller, W. An Introduction to Probability Theory and its Applications II. Wiley, New York, 1966.

    MATH  Google Scholar 

  3. Karlin, S. Stochastic Models and Optimal Policy for Selling an Asset, Chapter 9 in Studies in Applied Probability and Management Sciences. Stanford University Press, Stanford, CA, 1962.

    Google Scholar 

  4. Kurano, M., M. Yasuda, and J. Nakagami. Multi-Variate Stopping Problem with a Majority Rule. Journal of the Operations Research Society of Japan, 23, 205–223, 1980.

    MathSciNet  MATH  Google Scholar 

  5. Nash, J. Non-cooperative Game. Annals of Mathematics, 54, 286–295, 1951.

    Article  MathSciNet  MATH  Google Scholar 

  6. Presman, E. L. and I. M. Sonin. Equilibrium Points in a Game Related to the Best Choice Problem. Theory of Probability and its Applications, 20, 770–781, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  7. Sakaguchi, M. When to Stop: Randomly Appearing Bivariate Target Values. Journal of the Operational Research Society of Japan, 21,45–57, 1978.

    MathSciNet  MATH  Google Scholar 

  8. Szajowski, K. and M. Yasuda. Voting Procedure on Stopping Games of Markov Chain. In: Stochastic Modeling in Innovative Manufacturing (A. H. Christer, S. Osaki, and L. C. Thomas, eds.). Lecture Note in Economics and Mathematical System 445, Springer-Verlag, New York, 68–80,1997.

    Chapter  Google Scholar 

  9. Vorobév, N. N. Game Theory. Springer-Verlag, New York, 1977.

    Book  Google Scholar 

  10. Yasuda, M., J. Nakagami and M. Kurano. Multivariate Stopping Problem with a Monotone Rule, Journal of the Operational Research Society of Japan, 25,334–349, 1982.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Chiba University, Chiba, Japan

    Jun-ichi Nakagami, Masami Kurano & Masami Yasuda

Authors
  1. Jun-ichi Nakagami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masami Kurano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masami Yasuda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre for Industrial and Applicable Mathematics School of Mathematics, University of South Australia, 5000, Adelaide, SA, Australia

    Jerzy A. Filar

  2. School of Mathematics, University of South Australia, 5000, Adelaide, SA, Australia

    Vladimir Gaitsgory

  3. Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, 1-7-1, Kagamiyama, 739-8521, Higashi-Hiroshima City, Japan

    Koichi Mizukami

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media New York

About this paper

Cite this paper

Nakagami, Ji., Kurano, M., Yasuda, M. (2000). A Game Variant of the Stopping Problem on Jump Processes with a Monotone Rule. In: Filar, J.A., Gaitsgory, V., Mizukami, K. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 5. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1336-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1336-9_13

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7100-0

  • Online ISBN: 978-1-4612-1336-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation