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Minmax and maxmin of repeated games with incomplete information

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Abstract

For a class of 2-Person 0-sum repeated games with incomplete information,Aumann/Masch1er [1967] andStearns [1967] have given a necessary and sufficient condition for the existence of v∞ (the value of the infinitely repeated game).Mertens/Zamir [1971] andMertens [1971/72] have given the formula (and thus proved the existence) of\(\mathop {\lim }\limits_{n \to \infty } \) v n , the limit of the values of the games withn repetitions, for a much larger class of games than that treated byAumann/Maschler andSteams. In this paper we extend the Aumann-Maschler-Stearns results to the larger family of games studied byMertens [1971/72].

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References

  • Aumann, R.J., andM. Maschler: Repeated Games with Incomplete Information. A Survey of Recent Results. Report to the U.S. Arms Control and Disarmament Agency. Washington D.C. Final Report on Control ACDA/ST-116, prepared by Mathematica, Princeton, N.J., September 1967, Chapter III, 287–403.

  • -: Repeated Games with Incomplete Information. The Zero-Sum Extensive Case. Report to the U.S. Arms Control and Disarmament Agency. Washington D.C. Final Report on Contract ACDA/ST-143, prepared by Mathematica, Princeton, N.J., November 1968, Chapter II, 25–108.

  • Kohlberg, E., andS. Zamir: Repeated Games of Incomplete Information: The symmetric Case. The Annals of Statistics2, 1974, 1040–1041.

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  • Mertens, J.F.: The value of Two-Person Zero-Sum Repeated Games: The Extensive Case, International Journal of Game Theory1, 1971/72, 217–227.

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  • Mertens, J.F., andS. Zamir: The Value of Two-Person Zero-Sum Repeated Games with Lack of Information on Both Sides. International Journal of Game Theory1, 1971, 39–64.

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  • —: On a Repeated Game Without a Recursive Structure. International Journal of Game Theory5, 1977, 173–182.

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  • Stearns, R.E.: A Formal Information Concept for Games with Incomplete Information. Report to the U.S. Arms Control and Disarmament Agency. Washington D.C. Final Report on Contract ACDA/ST-116, prepared by Mathematica, Princeton, N.J., September 1967, Chapter IV, 405–433.

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Authors and Affiliations

  1. Center for Operations Research and Econometrics, University Catholique de Louvain, Core, 34 Voie du Roman Pays, Belgium

    J. -F. Mertens

  2. Statistics Dept., The Hebrew University, Jerusalem, Israel

    S. Zamir

Authors
  1. J. -F. Mertens
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  2. S. Zamir
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Mertens, J.F., Zamir, S. Minmax and maxmin of repeated games with incomplete information. Int J Game Theory 9, 201–215 (1980). https://doi.org/10.1007/BF01771426

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  • DOI: https://doi.org/10.1007/BF01771426

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