Matrix Games

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

Abstract

In the spirit of consulting the masters, we open this chapter with an example taken from von Neumann and Morgenstern (1944), who in turn got it from Sir Arthur Conan Doyle’s story The Final Solution:

Sherlock Holmes desires to proceed from London to Dover and hence to the Continent in order to escape from Professor Moriarty who pursues him. Having boarded the train he observes, as the train pulls out, the appearance of Professor Moriarty on the platform. Sherlock Holmes takes it for granted—and in this he is assumed to be fully justified—that his adversary, who has seen him, might secure a special train and overtake him. Sherlock Holmes is faced with the alternative of going to Dover or of leaving the train at Canterbury, the only intermediate station. His adversary—whose intelligence is assumed to be fully adequate to visualize these possibilities—has the same choice. Both opponents must choose the place of their detrainment in ignorance of the other’s corresponding decision. If, as a result of these measures, they should find themselves, in fine, on the same platform, Sherlock Holmes may with certainty expect to be killed by Moriarty. If Sherlock Holmes reaches Dover unharmed he can make good his escape.

Keywords

Defend Doyle Stake Undercut 

References

  1. Aumann, R., & Machsler, M. (1972). Some thoughts on the minimax principle. Management Science, 18(5-Part 2), 54–63.CrossRefGoogle Scholar
  2. Fréchet, M. (1953). Émile Borel, initiator of the theory of psychological games and its application. Econometrica, 21, 95–96.CrossRefGoogle Scholar
  3. Harsani, J. (1967). Games with incomplete information. Management Science, 14(3), 159–182.CrossRefGoogle Scholar
  4. Hofstadter, D. (1982). Mathemagical themas. Scientific American 16–18, August.Google Scholar
  5. Jain, M., Korzhyk, D., Vanek, O., Conitzer, V., Pechouochk, M., & Tambe, M. (2011). A double oracle algorithm for zero-sum security games on graphs. In The 10th International Conference on Autonomous Agents and Multiagent Systems (Vol. 1). International Foundation for Autonomous Agents and Multiagent Systems, Richland.Google Scholar
  6. Johnson, S. (1964). A search game. Advances in Game Theory (Vol. 52, p.39), Princeton University Press.Google Scholar
  7. Kaufman, H., & Lamb, J. (1967). An empirical test of game theory as a descriptive model. Perceptual and Motor Skills, 24(3), 951–960.CrossRefGoogle Scholar
  8. Kuhn, H., & Tucker, A. (Eds.) (1953). Contributions to the Theory of Games 2 (Annals of Mathematics Studies, Vol. 28), Princeton University Press.Google Scholar
  9. Lieberman, B. (1960). Human behavior in a strictly determined 3×3 matrix game. Behavioural Science, 5(4), 317–322.CrossRefGoogle Scholar
  10. Luce, R., & Raiffa, H. (1957). Games and Decisions. Wiley.Google Scholar
  11. Messick, D. (1967). Interdependent decision strategies in zero-sum games: a computer-controlled study. Behavioural Science, 12(1), 33–48.CrossRefGoogle Scholar
  12. Meinardi, J. (1964). A sequentially compounded search game. In A. Mensch, (Ed.), Proceedings of a conference under the aegis of the NATO Scientific Affairs Committee, Toulon, France (pp. 285–299), American Elsevier.Google Scholar
  13. Morin, R. (1960). Strategies in games with saddle points. Psychological Reports, 7(3), 479–483.CrossRefGoogle Scholar
  14. Pita, J., Jain, M., Marecki, J., Ordóñez, F., Portway, C., Tambe, M., Western, C., Paruchuri, P., & Kraus, S. (2008). Deployed ARMOR Protection: the application of a game theoretic model for security at the Los Angeles International Airport. Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems (pp. 125–132), International Foundation for Autonomous Agents and Multiagent Systems.Google Scholar
  15. Robinson, J. (1951). An iterative method of solving a game. Annals of Mathematics, 54(2), 296–301.CrossRefGoogle Scholar
  16. von Neumann, J. (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100 295–320. English translation in Contributions to the Theory of Games 4 13–42, Princeton University Press.Google Scholar
  17. von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behaviour, Princeton University 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