Every Normal-Form Game Has a Pareto-Optimal Nonmyopic Equilibrium

Steven Brams () and Mehmet S. Ismail

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Game theory; theory of moves; two-person games; cooperation (search for similar items in EconPapers)
JEL-codes: C70 D74 F50 (search for similar items in EconPapers)
Date: 2021-03-21
New Economics Papers: this item is included in nep-gth and nep-mic
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Journal Article: Every normal-form game has a Pareto-optimal nonmyopic equilibrium (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:106718

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