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Linear Mean-Field Games with Discounted Cost.

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Τίτλος: Linear Mean-Field Games with Discounted Cost.
Συγγραφείς: Saldi, Naci1 (AUTHOR) naci.saldi@bilkent.edu.tr
Πηγή: Mathematics of Operations Research (INFORMS). Feb2026, Vol. 51 Issue 1, p358-397. 40p.
Θεματικοί όροι: *Nash equilibrium, *Markov processes, *Distribution (Probability theory), *Cost
People: Nash, John F., 1928-2015
Περίληψη: In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. At every time, each agent is randomly coupled with another agent via their dynamics and one-stage cost function, where this randomization is generated via the empirical distribution of their states (i.e., the mean-field term). Therefore, the transition probability and the one-stage cost function of each agent depend linearly on the mean-field term, which is the key distinction between classical mean-field games and linear mean-field games. Under mild assumptions, we show that the policy obtained from infinite population equilibrium is ε(N) -Nash when the number of agents N is sufficiently large, where ε(N) is an explicit function of N. Then, using the linear programming formulation of Markov decision processes (MDPs) and the linearity of the transition probability in the mean-field term, we formulate the game in the infinite population limit as a generalized Nash equilibrium problem (GNEP) and establish an algorithm for computing equilibrium with a convergence guarantee. [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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  Data: Linear Mean-Field Games with Discounted Cost.
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Operations+Research+%28INFORMS%29%22">Mathematics of Operations Research (INFORMS)</searchLink>. Feb2026, Vol. 51 Issue 1, p358-397. 40p.
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  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="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br />*<searchLink fieldCode="DE" term="%22Cost%22">Cost</searchLink>
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  Data: In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. At every time, each agent is randomly coupled with another agent via their dynamics and one-stage cost function, where this randomization is generated via the empirical distribution of their states (i.e., the mean-field term). Therefore, the transition probability and the one-stage cost function of each agent depend linearly on the mean-field term, which is the key distinction between classical mean-field games and linear mean-field games. Under mild assumptions, we show that the policy obtained from infinite population equilibrium is ε(N) -Nash when the number of agents N is sufficiently large, where ε(N) is an explicit function of N. Then, using the linear programming formulation of Markov decision processes (MDPs) and the linearity of the transition probability in the mean-field term, we formulate the game in the infinite population limit as a generalized Nash equilibrium problem (GNEP) and establish an algorithm for computing equilibrium with a convergence guarantee. [ABSTRACT FROM AUTHOR]
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  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:
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    Identifiers:
      – Type: doi
        Value: 10.1287/moor.2023.0148
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 40
        StartPage: 358
    Subjects:
      – SubjectFull: Nash equilibrium
        Type: general
      – SubjectFull: Markov processes
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Cost
        Type: general
      – SubjectFull: Nash, John F., 1928-2015
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      – TitleFull: Linear Mean-Field Games with Discounted Cost.
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              Text: Feb2026
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              Y: 2026
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