Abstract

The asymptotic behavior of the solution of a differential inclusion provides a simple proof of a minmax theorem

Author information

Contact details are reproduced from the original publication and may be historical.

Ehud Lehrer

School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

lehrer@post.tau.ac.il

Sylvain Sorin

Equipe Combinatoire et Optimisation, UFR 929, Université P. et M. Curie, 175 Rue du Chevaleret, 75013 Paris, France
and: Lab. d'Econométrie, Ecole Polytechnique, 1 rue Descartes, 75005 Paris, France

sorin@math.jussieu.fr

References

  1. J.-P. Aubin, A. Cellina: Differential Inclusions, Springer, Berlin (1984).https://doi.org/10.1007/978-3-642-69512-4Google Scholar
  2. M. Benaim, J. Hofbauer, S. Sorin: Approximations and differential inclusions, SIAM J. Control Optimization 44 (2005) 328–348.https://doi.org/10.1137/S0363012904439301Google Scholar
  3. D. Blackwell: An analog of the minimax theorem for vector payoffs, Pac. J. Math. 6 (1956) 1–8.https://doi.org/10.2140/pjm.1956.6.1Google Scholar
  4. G. W. Brown, J. von Neumann: Solutions of games by differential equations, Ann. Math. Stud. 24 (1950) 73–79.https://doi.org/10.1515/9781400881727-007Google Scholar
  5. E. Lehrer: Allocation processes in cooperative games, Int. J. Game Theory 31 (2002) 341–351.https://doi.org/10.1007/s001820200123Google Scholar
  6. E. Lehrer, S. Sorin: Approachability and applications, manuscript (2000).Google Scholar
  7. J. Robinson: An iterative method of solving a game, Ann. Math. 54 (1951) 296–301.https://doi.org/10.2307/1969530Google Scholar
  8. G. V. Smirnov: Introduction to the Theory of Differential Inclusions, AMS, Providence (2002)https://doi.org/10.1090/gsm/041Google Scholar
  9. S. Sorin: A First Course on Zero-Sum Repeated Games, Springer, Paris (2002).Google Scholar

Suggested citation

E. Lehrer, S. Sorin. “Minmax via Differential Inclusion.” Journal of Convex Analysis 14 (2007), No. 2, 271–273. https://doi.org/10.68381/jca14019

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press.