Article
Pure strategy Nash equilibrium points and the Lefschetz fixed point theorem
International Journal of Game Theory
(1983)
Abstract
A pure strategy Nash equilibrium point existence theorem is established for a class ofn-person games with possibly nonacyclic (e.g. disconnected) strategy sets. The principal tool used in the proof is a Lefschetz fixed point theorem for multivalued maps, due to Eilenberg and Montgomery, which extends their better known. Eilenberg-Montgomery fixed point theorem (EMT) [Eilenberg/Montgomery, Theorem 1, p. 215] to nonacyclic spaces. Special cases of the existence theorem are also discussed.
Disciplines
Publication Date
1983
DOI
10.1007/BF01769884
Publisher Statement
This is a discussion paper of an article from International Journal of Game Theory 12 (1983): 181, doi:10.1007/BF01769884.
Citation Information
Leigh S. Tesfatsion. "Pure strategy Nash equilibrium points and the Lefschetz fixed point theorem" International Journal of Game Theory Vol. 12 Iss. 3 (1983) p. 181 - 191 Available at: http://works.bepress.com/leigh-tesfatsion/80/