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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
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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 N1, … , 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

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