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

Non-existence of super-additive solutions for 3-person games

  • 77 Accesses

  • 15 Citations

Abstract

The super-additive solution for 2-person Nash bargaining games (with constant threat) was defined axiomatically inPerles/Maschler [1981]. That paper contains also a study of its basic properties. In this paper we show that the axioms are incompatible even for 3-person unanimity games. This raises the problem of finding a satisfactory generalization of this solution concept to multi-person games.

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

References

  1. Grünbaum, B.: Convex Polytopes. Interscience Pub., Chichester 1967.

  2. Klee, V.L.: On Certain Intersection Properties of Convex Sets. Canadian J. Math.3, 1951, 272–275.

  3. Knaster, B., C. Kuratowski andS. Mazurkiewicz: Ein Beweis des Fixpunktsatzes fürn-dimensionale Simplexe. Fundamenta Mathematicae14, 1929, 132–137.

  4. Kohlberg, E., M. Maschler andM.A. Perles: Generalizing the Super-Additive Solution for Multi-Person Unanimity Games. To appear in 1983.

  5. Maschler, M., andM.A. Perles: The Present Status of the Super-Additive Solution. Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern. Ed. by R.J. Auman et al. Mannheim-Wien-Zürich 1981,103–110.

  6. Perles, M.A.: Non-Symmetric Super-Additive Solutions. To appear in 1983.

  7. -: Super-Additive Solutions without the Continuity Axiom. To appear in 1984.

  8. Perles, M.A., andM. Maschler: The Super-Additive Solution for the Nash Bargaining Game. International Journal of Game Theory10 (3/4), 1981, 163–193.

  9. Rockafellar, R.T.: Convex Analysis, Princeton 1970.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Perles, M.A. Non-existence of super-additive solutions for 3-person games. Int J Game Theory 11, 151–161 (1982). https://doi.org/10.1007/BF01755725

Download citation

Keywords

  • Economic Theory
  • Basic Property
  • Game Theory
  • Solution Concept
  • Bargaining Game