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Some Thoughts on the Minimax Principle

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Author Info

  • R. J. Aumann

    (The Hebrew University of Jerusalem)

  • M. Maschler

    (The Hebrew University of Jerusalem)

Abstract

It is generally agreed that the minimax solution to a two-person zero-sum matrix game is intuitively satisfactory. Now in many applications of game theory, a game is not described a priori in matrix (or "normal" or "strategic") form, but rather in extensive form, i.e., by its rules. A game described in such a way may be reduced to a matrix game by means of the concept of "strategy." If, moreover, it is of perfect recall, then all mixed strategies, and in particular the optimal strategies of each player, are equivalent to behavior strategies. The usual conclusion from these considerations is that for 2-person 0-sum games in extensive form, the minimax solution is intuitively satisfactory; and that in games of perfect recall, in particular, the players would do well to play in accordance with optimal (minimax) behavior strategies. In this paper we shall discuss some examples that, we believe, cast doubt on these conclusions.

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File URL: http://dx.doi.org/10.1287/mnsc.18.5.54
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 18 (1972)
Issue (Month): 5-Part-2 (January)
Pages: 54-63

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Handle: RePEc:inm:ormnsc:v:18:y:1972:i:5-part-2:p:54-63

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Cited by:
  1. Gregory B. Pollock & Antonio Cabrales, 1998. "Weak and strong altruism in traitgGroups: Reproductive suicide, personal fitness and expected value," Economics Working Papers 316, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Martin Shubik, 1988. "The Interaction of Implicit and Explicit Contracts in Repeated Agency," Cowles Foundation Discussion Papers 891, Cowles Foundation for Research in Economics, Yale University.
  3. Buechel, Berno & Emrich, Eike & Pohlkamp, Stefanie, 2013. "Nobody's innocent: the role of customers in the doping dilemma," MPRA Paper 44627, University Library of Munich, Germany.
  4. Vitaly Pruzhansky, 2011. "Some interesting properties of maximin strategies," International Journal of Game Theory, Springer, vol. 40(2), pages 351-365, May.
  5. Rapoport, Amnon & Amaldoss, Wilfred, 2000. "Mixed strategies and iterative elimination of strongly dominated strategies: an experimental investigation of states of knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 483-521, August.
  6. Robert W. Rosenthal, 1975. "An Arbitration Model for Normal-Form Games," Discussion Papers 121, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Vitaly Pruzhansky, 2004. "A Discussion of Maximin," Tinbergen Institute Discussion Papers 04-028/1, Tinbergen Institute.
  8. Souza, Filipe & Rêgo, Leandro, 2012. "Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable," MPRA Paper 43408, University Library of Munich, Germany.
  9. Kaneko, Mamoru, 1982. "Some remarks on the folk theorem in game theory," Mathematical Social Sciences, Elsevier, vol. 3(3), pages 281-290, October.
  10. Guillermo Owen, 2010. "Michael Maschler’s bibliography," International Journal of Game Theory, Springer, vol. 39(1), pages 301-308, March.
  11. Vitaly Pruzhansky, 2013. "Maximin play in completely mixed strategic games," Theory and Decision, Springer, vol. 75(4), pages 543-561, October.
  12. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, vol. 40(1), pages 123-146, July.
  13. HHironori Otsubo, 2012. "Contests with Incumbency Advantages: An Experiment Investigation of the Effect of Limits on Spending Behavior and Outcome," Jena Economic Research Papers 2012-020, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  14. repec:wyi:wpaper:002021 is not listed on IDEAS
  15. Vitaly Pruzhansky, 2003. "Maximin Play in Two-Person Bimatrix Games," Tinbergen Institute Discussion Papers 03-101/1, Tinbergen Institute.
  16. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, EconWPA, revised 18 Sep 1996.
  17. Vitaly Pruzhansky, 2004. "A Discussion of Maximin," Tinbergen Institute Discussion Papers 04-028/1, Tinbergen Institute.
  18. Vitaly Pruzhansky, 2003. "Maximin Play in Two-Person Bimatrix Games," Tinbergen Institute Discussion Papers 03-101/1, Tinbergen Institute.
  19. repec:fee:wpaper:1101 is not listed on IDEAS

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