Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Values of games with denumerably many players

  • 129 Accesses

  • 11 Citations

Abstract

In this paper axioms for values of games with denumerably many players are introduced and, on a certain space of games, a value is defined as a limit of values of finite games. Further, some relationships between the value that the topology on the space of games of bounded variation are investigated. It is also shown and the regular weighted majority games are members of the space on which the value is defined.

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

References

  1. Aumann, R. J. and L. S.Shapley: Values of Non-Atomic Games I: The Axiomatic Approach. Jerusalem RM 42 Dec. 1968; also The RAND Corporation RM-5468-PR, Nov. 1968.

  2. -: Values of Non-Atomic Games II: The Random Order Approach. The RAND Corporation RM-5842-PR, July 1969.

  3. -: Values of Non-Atomic Games III: Values and Derivatives. Jerusalem RM 49, Oct. 1969.

  4. -: Values of Non-Atomic Games IV: The Value and the Core. Jerusalem RM 51, Nov. 1969.

  5. Kannai, Y.: Values of Games with a Continuum of Players. Israel Jour. Math.4, 1966, 54–58.

  6. Owen, G.: A Note on theShapley Value. Management Sci.14, 1968, 731–732.

  7. Shapley, L. S.: A Value forn-Person Games. Contributions to the Theory of Games II; Princeton University Press, Princeton, 1953, 307–317.

  8. -: Values of Games with Infinitely Many Players. Recent Advances in Game Theory, Princeton University, May 1962, 113–118. (Papers delivered at a meeting of the Princeton University Conference, in October 1961, privately printed for members of the conference.)

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Artstein, Z. Values of games with denumerably many players. Int J Game Theory 1, 27–37 (1971). https://doi.org/10.1007/BF01753432

Download citation

Keywords

  • Economic Theory
  • Game Theory
  • Bounded Variation
  • Weighted Majority
  • Majority Game