Tenable threats when Nash Equilibrium is the norm

Françoise Forges; Jozsef Sakovics

doi:10.1007/s00182-022-00806-3

Tenable threats when Nash Equilibrium is the norm

Françoise Forges^*, Jozsef Sakovics

^*Corresponding author for this work

School of Economics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis.

Original language	English
Pages (from-to)	589-605
Number of pages	21
Journal	International Journal of Game Theory
Volume	51
Issue number	3-4
Early online date	14 Sept 2022
DOIs	https://doi.org/10.1007/s00182-022-00806-3
Publication status	Published - Nov 2022

Keywords / Materials (for Non-textual outputs)

game theory
microeconomics
backward induction
credible threat
equilibrium refinement
sequential rationality
games of perfect information

Access to Document

10.1007/s00182-022-00806-3

ForgesF&SakovicsJIJGT2022TenableThreatsWhenNashAccepted author manuscript, 233 KBLicence: Creative Commons: Attribution (CC-BY)

1 Discussion paper

Tenable threats when Nash Equilibrium is the norm
Sakovics, J. & Forges, F., 11 Jun 2021, Edinburgh School of Economics, University of Edinburgh, p. 1-21, 21 p. (Edinburgh School of Economics Discussion Paper Series; no. 301).
Research output: Working paper › Discussion paper

Cite this

@article{1aeb6dc33b384894aef20eb25fd985a5,

title = "Tenable threats when Nash Equilibrium is the norm ",

abstract = "We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis.",

keywords = "game theory, microeconomics, backward induction, credible threat, equilibrium refinement, sequential rationality, games of perfect information",

author = "Fran{\c c}oise Forges and Jozsef Sakovics",

note = "Funding Information: We are grateful for helpful comments from Rabah Amir, Dietmar Berwanger, Helmut Bester, Roberto Burguet, Martin Cripps, Eric van Damme, Drew Fudenberg, Itzhak Gilboa, Morgan Patty, Klaus Ritzberger, Andr{\'e}s Salamanca, Larry Samuelson, Joel Sobel, Robert Wilson, Eyal Winter, Gabriel Ziegler and (virtual) audiences at Universit{\`a} Bocconi and University of Edinburgh. S{\'a}kovics acknowledges financial support from the Spanish Government through a Beatriz Galindo grant (BG20/00079) and Grant PID2020-115018RB-C33 funded by MCIN/AEI/10.13039/501100011033. For the purpose of open access, the second author has applied a {\textquoteleft}Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission{\textquoteright}.",

year = "2022",

month = nov,

doi = "10.1007/s00182-022-00806-3",

language = "English",

volume = "51",

pages = "589--605",

journal = "International Journal of Game Theory",

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number = "3-4",

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TY - JOUR

T1 - Tenable threats when Nash Equilibrium is the norm

AU - Forges, Françoise

AU - Sakovics, Jozsef

N1 - Funding Information: We are grateful for helpful comments from Rabah Amir, Dietmar Berwanger, Helmut Bester, Roberto Burguet, Martin Cripps, Eric van Damme, Drew Fudenberg, Itzhak Gilboa, Morgan Patty, Klaus Ritzberger, Andrés Salamanca, Larry Samuelson, Joel Sobel, Robert Wilson, Eyal Winter, Gabriel Ziegler and (virtual) audiences at Università Bocconi and University of Edinburgh. Sákovics acknowledges financial support from the Spanish Government through a Beatriz Galindo grant (BG20/00079) and Grant PID2020-115018RB-C33 funded by MCIN/AEI/10.13039/501100011033. For the purpose of open access, the second author has applied a ‘Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission’.

PY - 2022/11

Y1 - 2022/11

N2 - We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis.

AB - We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis.

KW - game theory

KW - microeconomics

KW - backward induction

KW - credible threat

KW - equilibrium refinement

KW - sequential rationality

KW - games of perfect information

U2 - 10.1007/s00182-022-00806-3

DO - 10.1007/s00182-022-00806-3

M3 - Article

SN - 0020-7276

VL - 51

SP - 589

EP - 605

JO - International Journal of Game Theory

JF - International Journal of Game Theory

IS - 3-4

ER -

Tenable threats when Nash Equilibrium is the norm

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Keywords / Materials (for Non-textual outputs)

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Research output

Tenable threats when Nash Equilibrium is the norm

Cite this