Skip to main content
Log in

Some recent results inn-person game theory

  • Published:
Mathematical Programming Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The discussion will center mainly on some work on two solution concepts: the core for gaines without side payments and the nucleolus for games with side payments (characteristic funtion games). The core has become an important equilibrium concept in mathematical economics. The nucleolus is related to the theory of bargaining sets.

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

  1. L.J.Billera, “Some theorems on the core of ann-person game without side payments”,SIAM Journal of Applied Mathematics 18 (1970) 567–579.

    Google Scholar 

  2. O.N.Bondareva, “Some applications of linear programming methods to the theory of cooperative games”,Problemy Kibernet. 10 (1963) 119–139.

    Google Scholar 

  3. A.Charnes, M.Eisner and K.O.Kortanek, “On weakly balanced games and duality theory”,Cahiers du Centre D'Etudes De Recherche Opérationelle 12 (1970) 7–21.

    Google Scholar 

  4. A.Charnes and K.Kortanek, “On classes of convex and preemptive nuclei forn-person games”,Proc. 1967 Princeton Mathematical Programming Symposium, ed. H.W. Kuhn (Princeton University Press, Princeton, 1970) pp. 377–390.

    Google Scholar 

  5. A.Charnes and K.Kortanek, “On asymptotic behavior of some nuclei ofn-person games and the piecewise linearity of the nucleolus”, Management Science Research Report No. 170, Carnegie-Mellon University (August, 1969).

  6. M.Eisner, “On duality in infinite-player games and sequential chance-constrained programming”, Ph. D. thesis, Department of Operations Research, Cornell University (January, 1970).

  7. J.Grotte, “Computation of and observations on the nucleolus, the normalized nucleolus, and the central games”, M.S. thesis, Field of Applied Mathematics, Cornell University (September, 1970).

  8. Y. Kannai, “Countably additive measures in cores of games”,Journ. Math. Anal. and Applic. 27 (1969) 227–240.

    Google Scholar 

  9. M.Keane, “Some topics inn-person game theory”, Ph.D. thesis, Northwestern University (June, 1969).

  10. E.Kohlberg, “On the nucleolus of a characteristic function game”, Research memorandum No. 48, Department of Mathematics, The Hebrew University of Jerusalem (July, 1969). (To appear inSIAM Journal of Applied Mathematics).

  11. E.Kohlberg, “The nucleolus as a solution of a minimization problem”, to appear.

  12. A.Kopelowitz, “Computation of the kernels of simpel games and the nucleolus ofn-person games”, Research Memorandum No. 31, Department of Mathematics, The Hebrew University of Jerusalem (September, 1967).

  13. M.Maschler, B.Peleg and L.S.Shapley, “The kernel and the nucleolus of a cooperative game as locuses in the strong-core”, Research Memorandum No. 60, Department of Mathematics, The Hebrew University of Jerusalem (May, 1970).

  14. H.Scarf, “The core of ann-person game”,Econometrica 35 (1967) 50–69.

    Google Scholar 

  15. D. Schmeidler, “The nucleolus of a characteristic funtion game”,SIAM Journal of Applied Mathematics 17 (1969) 1163–1170.

    Google Scholar 

  16. D.Schmeidler, “On balanced games with infinitely many players”, Research Memorandum No. 28, Department of Mathematics, The Hebrew University of Jerusalem (June, 1967).

  17. L.Shapley, “On balanced sets and scores”.Naval Research Logistics Quarterly 14 (1967) 453–460.

    Google Scholar 

  18. L.Shapley, “Balanced sets, Sperner's lemma, and Scarf's theorem on the core”, informal lecture at the Second International Game Theory Workshop, Berkeley, August, 1970. To appear (RAND Corporation, Santa Monica, California).

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported by the National Science Foundation under grant GK-4795.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Billera, L.J. Some recent results inn-person game theory. Mathematical Programming 1, 58–67 (1971). https://doi.org/10.1007/BF01584072

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01584072

Keywords

Navigation