Markov (Multistage) Games

  • Alan Washburn
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 201)


In games that involve a sequence of moves, it can be useful to regard certain payoffs as themselves being games, and those payoffs might in turn have other games as payoffs, or possibly even the original game as a payoff. The idea of representing a game in this manner is often parsimonious and natural. The Inspection Game is a prototype.


Differential Game Stochastic Game Tree Game Ground Support Graphical Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Baston, V., & Bostok, F. (1993). Infinite deterministic graphical games. SIAM J. Control and Optimization, 31(6), 1623–1629.CrossRefGoogle Scholar
  2. Berkovitz, L., & Dresher, M. (1959). A game theory analysis of tactical air war. Operations Research, 7(5), 599–620.CrossRefGoogle Scholar
  3. Blackwell, D. (1954). On multi-component attrition games. Naval Research Logistics, 1(3), 210–16.CrossRefGoogle Scholar
  4. Dresher, M. 1962 A sampling inspection problem in arms control agreements: a game theory approach. Memorandum RM-2972-ARPA, RAND, Santa Monica, CA.Google Scholar
  5. Everett, H. 1957 Recursive games. Contributions to the theory of games III (Ann. Math. Studies 39, eds. M. Dresher, A. Tucker, and P. Wolfe) 47–78, Princeton U. Press.Google Scholar
  6. Ferguson, T., & Melolidakis, C. (1998). On the inspection game. Naval Research Logistics, 45(3), 327–334.CrossRefGoogle Scholar
  7. Friedman, Y. (1977). Optimal strategy for the one-against-many battle. Operations Research, 25(5), 884–888.CrossRefGoogle Scholar
  8. Gale, D. and F. Stewart 1953. Infinite games with perfect information. Contributions to the theory of games II (Ann. Math. Studies 28, eds. H. Kuhn and A. Tucker), Princeton U. Press.Google Scholar
  9. Guy, R. (Ed.). (1991). Combinatorial Games. Rhode Island: American Mathematical Society.Google Scholar
  10. Ho, Y., Bryson, A., & Baron, S. (1965). Differential games and optimal pursuit-evasion strategies. IEEE Transactions on Automatic Control, 10(4), 385–389.CrossRefGoogle Scholar
  11. Isaacs, R. 1965. Differential Games, Wiley.Google Scholar
  12. Isbell, J., & Marlow, W. (1956). Attrition games. Naval Research Logistics, 3(1–2), 71–94.CrossRefGoogle Scholar
  13. Isler, V., Kannan, S., & Khanna, S. (2005). Randomized pursuit-evasion in a polygonal environment. IEEE Transactions on Robotics, 5(21), 864–875.Google Scholar
  14. Kikuta, K. (1983). A note on the one-against-many battle. Operations Research, 31(5), 952–956.CrossRefGoogle Scholar
  15. Kikuta, K. (1986). The matrix game derived from the many-against-many battle. Naval Research Logistics, 33(4), 603–612.CrossRefGoogle Scholar
  16. Ladany, S. and R. Machol (eds.) 1977. Optimal Strategies in Sports. North Holland.Google Scholar
  17. Mertens, J., & Neyman, A. (1981). Stochastic games have a value. Int. J. of Game Theory, 10(1), 53–66.CrossRefGoogle Scholar
  18. Owen, G. 1995. Game Theory (third edition). Academic Press.Google Scholar
  19. Pultr, A. and F. Morris 1984. Prohibiting repetition makes playing games substantially harder. Intl. J. Game Theory 13 27–40.Google Scholar
  20. Raghavan, T., & Filar, J. (1991). Algorithms for stochastic games–a survey. Methods and Models of Operations Research, 35(6), 437–472.Google Scholar
  21. Schwartz, E. (1979). An improved computational procedure for optimal allocation of aircraft sorties. Operations Research, 27(3), 621–627.CrossRefGoogle Scholar
  22. Shilov, G. 1965. Mathematical Analysis 44–45, Pergamon.Google Scholar
  23. Thomas, C., & Deemer, W. (1957). The role of operational gaming in operations research. Operations Research, 5(1), 1–27.CrossRefGoogle Scholar
  24. U.S. Air Force (Studies and Analysis). 1971. Methodology for use in measuring the effectiveness of general purpose forces (an algorithm for approximating the game theoretical value of N-staged games). Report Saber Grand (Alpha).Google Scholar
  25. Washburn, A. (1990). Deterministic graphical games. Journal of Mathematical Analysis and Applications., 153(1), 84–96.CrossRefGoogle Scholar
  26. Winston, W. 2009. Mathletics. Princeton U. Press.Google Scholar
  27. Zermelo, E. 1912. Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. Proceedings of the fifth International Congress of Mathematicians, 501–510, Cambridge U. Press.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Alan Washburn
    • 1
  1. 1.Operations Research DepartmentNaval Postgraduate SchoolMontereyUSA

Personalised recommendations