Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T06:05:55.733Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium Points for Open Acyclic Relations

Published online by Cambridge University Press:  20 November 2018

Bezalel Peleg
Bezalel Peleg*
Affiliation:
The University of Michigan, Ann Arbor, Michigan and The Hebrew University of Jerusalem, Israel
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A formulation of a fixed point theorem, which can be applied conveniently to non-cooperative games and cooperative games, is suggested in this note.

Let N 1, … , Nm be m non-empty, finite disjoint sets. For k = 1, … , m we denote by Sk the simplex the coordinates of whose points are indexed by the members of Nk ; thus Sk is the collection of all real functions xk defined on Nk which satisfy:

1.1

1.2

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967, pp. 366 - 369
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Davis, M. and Maschler, M., The kernel of a cooperative game, Econometric Research Program, Research Memorandum No. 58 (1963), Princeton University, Princeton, N.J. ; to appear in Naval Logistics Quarterly.Google Scholar
2. Davis, M. and Maschler, M., Existence of stable payoff configurations for cooperative games, Bull. Amer. Math. Soc., 69 (1963), 106–108.Google Scholar
3. Nash, J. F., Non cooperative games, Ann. Math., 54 (1951), 286–295.Google Scholar
4. Peleg, B., Existence theorem for the bargaining set M1 (i)), Bull. Amer. Math. Soc., 69 (1963), 109–110.Google Scholar