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

TY - JOUR

T1 - Every normal-form game has a Pareto-optimal nonmyopic equilibrium

AU - Brams, Steven J.

AU - Ismail, Mehmet S.

N1 - Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/5/16

Y1 - 2021/5/16

N2 - 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.

AB - 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.

KW - Cooperation

KW - Dynamic analysis of games

KW - Farsightedness

KW - Game theory

KW - Nonmyopic equilibrium

UR - http://www.scopus.com/inward/record.url?scp=85108099477&partnerID=8YFLogxK

U2 - 10.1007/s11238-021-09824-1

DO - 10.1007/s11238-021-09824-1

M3 - Article

AN - SCOPUS:85108099477

SN - 0040-5833

VL - 92

JO - THEORY AND DECISION

JF - THEORY AND DECISION

IS - 2

ER -