Academic Journal
Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games.
| Τίτλος: | Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games. |
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| Συγγραφείς: | Cohen, Asaf1 (AUTHOR) asafc@umich.edu, Zell, Ethan1 (AUTHOR) ezell@umich.edu |
| Πηγή: | Mathematics of Operations Research (INFORMS). May2026, Vol. 51 Issue 2, p1139-1173. 35p. |
| Θεματικοί όροι: | *Nash equilibrium, *Markov processes, *Game theory, Finite state machines, Hamilton-Jacobi-Bellman equation, Large deviation theory, Galerkin methods, Cost functions |
| People: | Nash, John F., 1928-2015 |
| Περίληψη: | Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric n-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian strategies, we first prove that any solution to the MFG system gives rise to a (C/n) -Nash equilibrium in the n-player game. We follow this result by proving the same is true for the strategy profile derived from the master equation. We conclude the main theoretical portion of the paper by establishing a large deviation principle for empirical measures associated with the asymptotic Nash equilibria. Then, we contrast the asymptotic Nash equilibria using an example. We solve the MFG system directly and numerically solve the ergodic master equation by adapting the deep Galerkin method. We use these results to derive the strategies of the asymptotic Nash equilibria and compare them. Finally, we derive an explicit form for the rate functions in dimension two. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cohen%2C+Asaf%22">Cohen, Asaf</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> asafc@umich.edu</i><br /><searchLink fieldCode="AR" term="%22Zell%2C+Ethan%22">Zell, Ethan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ezell@umich.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Operations+Research+%28INFORMS%29%22">Mathematics of Operations Research (INFORMS)</searchLink>. May2026, Vol. 51 Issue 2, p1139-1173. 35p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Nash+equilibrium%22">Nash equilibrium</searchLink><br />*<searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br />*<searchLink fieldCode="DE" term="%22Game+theory%22">Game theory</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+state+machines%22">Finite state machines</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton-Jacobi-Bellman+equation%22">Hamilton-Jacobi-Bellman equation</searchLink><br /><searchLink fieldCode="DE" term="%22Large+deviation+theory%22">Large deviation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink> – Name: SubjectPerson Label: People Group: Su Data: <searchLink fieldCode="PE" term="%22Nash%2C+John+F%2E%2C+1928-2015%22">Nash, John F., 1928-2015</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric n-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian strategies, we first prove that any solution to the MFG system gives rise to a (C/n) -Nash equilibrium in the n-player game. We follow this result by proving the same is true for the strategy profile derived from the master equation. We conclude the main theoretical portion of the paper by establishing a large deviation principle for empirical measures associated with the asymptotic Nash equilibria. Then, we contrast the asymptotic Nash equilibria using an example. We solve the MFG system directly and numerically solve the ergodic master equation by adapting the deep Galerkin method. We use these results to derive the strategies of the asymptotic Nash equilibria and compare them. Finally, we derive an explicit form for the rate functions in dimension two. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/moor.2024.0478 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 1139 Subjects: – SubjectFull: Nash equilibrium Type: general – SubjectFull: Markov processes Type: general – SubjectFull: Game theory Type: general – SubjectFull: Finite state machines Type: general – SubjectFull: Hamilton-Jacobi-Bellman equation Type: general – SubjectFull: Large deviation theory Type: general – SubjectFull: Galerkin methods Type: general – SubjectFull: Cost functions Type: general – SubjectFull: Nash, John F., 1928-2015 Type: general Titles: – TitleFull: Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cohen, Asaf – PersonEntity: Name: NameFull: Zell, Ethan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0364765X Numbering: – Type: volume Value: 51 – Type: issue Value: 2 Titles: – TitleFull: Mathematics of Operations Research (INFORMS) Type: main |
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