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

  • Jun-ichi Nakagami
  • Masami Kurano
  • Masami Yasuda
Conference paper
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 5)


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.


Equilibrium Strategy Jump Process Noncooperative Game Borel Measurable Function Unanimity Rule 
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  1. [1]
    Bellman, R. Stability Theory of Differential Equations. McGraw-Hill, New York, 1953.MATHGoogle Scholar
  2. [2]
    Feller, W. An Introduction to Probability Theory and its Applications II. Wiley, New York, 1966.MATHGoogle Scholar
  3. [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. [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.MathSciNetMATHGoogle Scholar
  5. [5]
    Nash, J. Non-cooperative Game. Annals of Mathematics, 54, 286–295, 1951.MathSciNetMATHCrossRefGoogle Scholar
  6. [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.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Sakaguchi, M. When to Stop: Randomly Appearing Bivariate Target Values. Journal of the Operational Research Society of Japan, 21,45–57, 1978.MathSciNetMATHGoogle Scholar
  8. [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.CrossRefGoogle Scholar
  9. [9]
    Vorobév, N. N. Game Theory. Springer-Verlag, New York, 1977.CrossRefGoogle Scholar
  10. [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.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Jun-ichi Nakagami
    • 1
  • Masami Kurano
    • 1
  • Masami Yasuda
    • 1
  1. 1.Department of Mathematics and InformaticsChiba UniversityChibaJapan

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