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Every normal-form game has a Pareto-optimal nonmyopic equilibrium

Research output: Contribution to journalArticlepeer-review

Steven J. Brams, Mehmet S. Ismail

Original languageEnglish
JournalTHEORY AND DECISION
DOIs
Accepted/In press2021

Bibliographical note

Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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Abstract

It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis.

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