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

Steven Brams () and Mehmet S. Ismail ()
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Mehmet S. Ismail: King’s College London

Theory and Decision, 2022, vol. 92, issue 2, No 4, 349-362

Abstract: 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: Farsightedness; Nonmyopic equilibrium; Cooperation; Game theory; Dynamic analysis of games (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11238-021-09824-1

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