Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T17:40:36.628Z Has data issue: false hasContentIssue false
  • English
  • Français

On a discrete-time non-zero-sum Dynkin problem with monotonicity

Published online by Cambridge University Press:  14 July 2016

Yoshio Ohtsubo
Yoshio Ohtsubo*
Affiliation:
Kyushu Institute of Technology
*
∗Postal address: Department of Electric, Electronic and Computer Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a monotone case of the non-zero-sum stopping game with discrete time parameter which is called the Dynkin problem. Marner (1987) has investigated a stopping game with general monotone reward structures, but his monotonicity is too strong to apply our problem. We establish that there exists an explicit equilibrium point in our monotone case. We also give a simple example applicable to a duopolistic exit game.

Keywords

STOPPING GAMEDYNKIN PROBLEMEQUILIBRIUM POINTMONOTONE CASE
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 466 - 472
Copyright
Copyright © Applied Probability Trust 1991 

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.)

References

[1]Bensoussan, A. and Friedman, A. (1977) Non-zero-sum stochastic differential games with stopping times and free boundary problems. Trans. Amer. Math. Soc. 231, 275–327.10.1090/S0002-9947-1977-0453082-7Google Scholar
[2]Chow, Y., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton-Mifflin, Boston.Google Scholar
[3]Dynkin, E. B. (1969) Game variant of a problem on optimal stopping. Soviet Math. Dokl. 10, 270–274.Google Scholar
[4]Huang, Chi-Fu and Li, L. (1990) Continuous time stopping games with monotone reward structures. Math. Operat. Res. 15, 496–507.10.1287/moor.15.3.496Google Scholar
[5]Mamer, J. W. (1987) Monotone stopping games. J. Appl. Prob. 24, 386–401.10.2307/3214263Google Scholar
[6]Morimoto, H. (1986) Non-zero-sum discrete parameter stochastic games with stopping times. Prob. Theory Rel. Fields 72, 155–160.10.1007/BF00343901Google Scholar
[7]Morimoto, H. (1986) On noncooperative n-player cyclic stopping games. Stochastics 20, 27–37.Google Scholar
[8]Nagai, H. (1988) Nonzero-sum stopping games of symmetric Markov processes. Prob. Theory Rel. Fields 75, 487–497.10.1007/BF00320329Google Scholar
[9]Neveu, J. (1975) Discrete-Parameter Martingales. North-Holland, Amsterdam.Google Scholar
[10]Ohtsubo, Y. (1987) A nonzero-sum extension of Dynkin's stopping problem. Math. Operat. Res. 12, 277–296.10.1287/moor.12.2.277Google Scholar