Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T17:38:56.735Z Has data issue: false hasContentIssue false
  • English
  • Français

Zero-sum two-person semi-Markov games

Published online by Cambridge University Press:  14 July 2016

Arbind K. Lal  and
Sagnik Sinha
Arbind K. Lal*
Affiliation:
Indian Statistical Institute
Sagnik Sinha*
Affiliation:
Indian Statistical Institute
*
Postal address for both authors: Indian Statistical Institute, New Delhi 110016, India.
Postal address for both authors: Indian Statistical Institute, New Delhi 110016, India.
Get access Rights & Permissions [Opens in a new window]

Abstract

Semi-Markov games are investigated under discounted and limiting average payoff criteria. The issue of the existence of the value and a pair of stationary optimal strategies are settled; the optimality equation is studied and under a natural ergodic condition the existence of a solution to the optimality equation is proved for the limiting average case. Semi-Markov games provide useful flexibility in constructing recursive game models. All the work on Markov/semi-Markov decision processes and Markov (stochastic) games can be viewed as special cases of the developments in this paper.

Keywords

STOCHASTIC GAMESPAYOFF CRITERIONSEMI-MARKOV DECISION PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 56 - 72
Copyright
Copyright © Applied Probability Trust 1992 

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

∗

Supported by a research grant from the University Grants Commission, India.

∗∗

Supported by a research grant from the National Board of Higher Mathematics, Tata Institute of Fundamental Research, India.

References

Federgruen, A. and Tijms, H. C. (1978) The optimality equation in average cost denumerable semi-Markov decision problems, recurrency conditions and algorithms. J. Appl. Prob. 15, 356–373.Google Scholar
Federgruen, A., Hordijk, A. and Tijms, H. C. (1978) A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices. J. Appl. Prob. 15, 842–847.Google Scholar
Hordijk, A. (1974) Dynamic Programming and Markov Potential Theory. Mathematical Centre Tract 51, Mathematisch Centrum, Amsterdam.Google Scholar
Howard, R. D. (1971) Dynamic Probabilistic Systems, Vol. II, Semi-Markov and Decision Processes. Wiley, New York.Google Scholar
Kirman, A. P. and Sobel, M. J. (1974) Dynamic oligopoly with inventories. Econometrica 42, 279–287.Google Scholar
Kuhn, H. W. (1953) Extensive games and the problem of information. In Contributions to the Theory of Games. Vol. II, ed. Kuhn, H. W. and Tucker, A. W., Ann. Math. Stud. 28, 193–216, Princeton University Press.Google Scholar
Parthasarthy, T. (1973) Discounted, positive and noncooperative stochastic games. Int. J. Game Theory 2, 25–37.Google Scholar
Raut, L. K. (1990) Two-sided altruism, Lindhal equilibrium and Pareto efficiency in overlapping generations models. Discussion paper 90-97, Economics Department, University of California, San Diego.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Schweitzer, P. J. (1971) Iterative solutions of functional equations of undiscounted Markov renewal programming. J. Math. Anal. Appl. 34, 495–501.Google Scholar
Shapley, L. (1953) Stochastic games. Proc. Natl. Acad. Sci. U.S.A. 39, 1095–1100.Google Scholar
Vrieze, O. J. (1983) Stochastic Games with Finite State and Action Spaces, Ph.D. Dissertation. Mathematical Centre, Amsterdam.Google Scholar