Hostname: page-component-84b7d79bbc-5lx2p Total loading time: 0 Render date: 2024-07-28T05:38:07.533Z Has data issue: false hasContentIssue false
  • English
  • Français

Monotone stopping games

Published online by Cambridge University Press:  14 July 2016

John W. Mamer
John W. Mamer*
Affiliation:
University of California, Los Angeles
*
∗Postal address: Graduate School of Management, UCLA, Los Angeles, CA 90024, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the extension of optimal stopping problems to non-zero-sum strategic settings called stopping games. By imposing a monotone structure on the pay-offs of the game we establish the existence of a Nash equilibrium in non-randomized stopping times. As a corollary, we identify a class of games for which there are Nash equilibria in myopic stopping times. These games satisfy the strategic equivalent of the classical ‘monotone case' assumptions of the optimal stopping problem.

Keywords

NON-COOPERATIVE GAMESNASH EQUILIBRIAMYOPIC STOP RULES
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 386 - 401
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported by a grant from the Research Project in Managerial Economics and Public Policy, UCLA Graduate School of Management.

References

[1] Chaput, H. (1974) Markov games. Technical Report No. 33, Dept. of Operations Research, Stanford University.Google Scholar
[2] Chow, Y., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton-Mifflin, Boston.Google Scholar
[3] Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
[4] Derman, C. (1963) On optimal replacement rules when changes of state are Markovian. In Mathematical Optimization Techniques, ed. Bellman, R., University of California Press, Berkeley.Google Scholar
[5] Dynkin, E. (1969) Game variant of a problem on optimal stopping. Soviet Math. Dokl. 10, 270–274.Google Scholar
[6] Klass, M. (1973) Properties of optimal extended-value stop rules Sn/n. Ann. Prob. 1, 719–758.Google Scholar
[7] Lepeltier, J. and Maingueneau, M. (1983) Jeu de Dynkin avec Coût dépendant d'une Stratégie continue. Lecture Notes in Control and Information 61, Springer-Verlag, Berlin.Google Scholar
[8] Lippman, S. and Mccall, J. (1976) The economics of job search: a survey. Economic Enquiry 14, 155–189.Google Scholar
[9] Reinganum, J. (1982) Strategic search theory. Internat. Econom. Rev. 23, 1–17.Google Scholar
[10] Rothschild, M. (1974) Searching for the lowest price when the distribution of price is unknown. J. Political Economy 82, 689–712.Google Scholar
[11] Tarski, A. (1955) A lattice theoretic fixed point theorem. Pacific J. Math. 5, 285–309.Google Scholar