Pure strategy Nash equilibrium points and the Lefschetz fixed point theorem

Leigh Tesfatsion ()

International Journal of Game Theory, 1983, vol. 12, issue 3, 191 pages

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. Copyright Physica-Verlag 1983

Date: 1983
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Working Paper: Pure Strategy Nash Equilibrium Points and the Lefschetz Fixed Point Theorem (1983)
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DOI: 10.1007/BF01769884

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