Skip to main content
Log in

“Big Match” with lack of information on one side (part i)

  • Papers
  • Published:
International Journal of Game Theory Aims and scope Submit manuscript

Abstract

For a special class of two-person zero-sum infinitely repeated stochastic games with incomplete information, we prove the existence of the maxmin, minmax and limΝ n . However the value may not exist and moreover maxmin and limΝ n may be transcendental functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aumann, R.J.: Mixed and behavior strategies in infinite extensive games. In: Advances in Game Theory. Ed. by M. Dresher, L.S. Shapley and A.W. Tucker. Princeton 1964, 627–650.

  • —: Agreeing to disagree. Annals of Statistics4, 1974. 1236–1239.

    Google Scholar 

  • Aumann, R.J., andM. Maschler: Game theoretic aspects of gradual disarmament. Chapter V of Development of Utility Theory for Arms Control and Disarmament. Report to the U.S. A.C.D.A., Contract S.T. 80, Mathematica, Princeton 1966.

    Google Scholar 

  • —: Repeated games of incomplete information: the zero-sum extensive case. Chapter III of The Indirect Measurement of Utility. Report to the U.S. A.C.D.A., Contract ST 140, Mathematica, Princeton 1968.

    Google Scholar 

  • Bewley, T., andE. Kohlberg: The asymptotic theory of stochastic games. Mathematics of Operations Research1, 1976, 197–208.

    Google Scholar 

  • Blackwell, D., andT.S. Ferguson: The Big Match. Annals of Mathematical Statistics39, 1968, 159–163.

    Google Scholar 

  • Kohlberg, E.: Repeated games with absorbing states. Annals of Statistics2, 1974, 724–738.

    Google Scholar 

  • Kohlberg, E., andS. Zamir: Repeated games of incomplete information; the symmetric case. Annals of Statistics2, 1974, 1040–1041.

    Google Scholar 

  • Kuhn, H.W.: Extensive games and the problem of information. In: Contribution to the Theory of Games II. Ed. by H.W. Kuhn and A.W. Tucker. Princeton University Press, 1953, 193–216.

  • Mertens, J.F., andA. Neyman: Stochastic games. International Journal of Game Theory10, 1981, 53–66.

    Google Scholar 

  • 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, 1971–1972, 39–64.

    Google Scholar 

  • —: On a repeated game without a recursive structure. International Journal of Game Theory5, 1976, 173–182.

    Google Scholar 

  • —: Minmax and maxmin of repeated games with incomplete information. International of Game Theory9, 1980, 201–215.

    Google Scholar 

  • —: Incomplete information games with transcendental values. Mathematics of Operations Research6, 1981, 313–318.

    Google Scholar 

  • Sion, M.: On general minimax theorems. Pacific Journal of Mathematics8, 1958, 171–176.

    Google Scholar 

  • Sorin, S.: Une introduction aux jeux répétés à deux joueurs, à somme nulle et à information incomplète. Cahiers de Mathématiques Economiques nℴ 1, Université Paris 6, 1979 (English version, IMSSS, Stanford, T.R. 312, 1980).

  • —: Repeated games with incomplete information and absorbing states: two examples. Report nℴ 16/80, Institute for Advanced Studies, Jerusalem 1980.

    Google Scholar 

  • -: Big Match with lack of information on one side. CORE Discussion Paper 8133, 1981.

  • -: Big Match with lack of information on one side (Part II). CORE Discussion Paper 8229, 1982, forthcoming in International Journal of Game Theory.

  • Waternaux, C.: Solution for a class of repeated games without a recursive structure. International Journal of Game Theory12, 1983, 129–160.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sorin, S. “Big Match” with lack of information on one side (part i). Int J Game Theory 13, 201–255 (1984). https://doi.org/10.1007/BF01769463

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01769463

Keywords

Navigation