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A myopic adjustment process for mean field games with finite state and action space

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  • Berenice Anne Neumann

    (Trier University)

Abstract

In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations is the complexity of the computations necessary to determine dynamic mean field equilibria, which makes it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards strict stationary equilibria under rather broad conditions. Moreover, we also obtain a global convergence result under stronger, yet intuitive conditions.

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  • Berenice Anne Neumann, 2024. "A myopic adjustment process for mean field games with finite state and action space," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(1), pages 159-195, March.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:1:d:10.1007_s00182-023-00866-z
    DOI: 10.1007/s00182-023-00866-z
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    References listed on IDEAS

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    1. V. N. Kolokoltsov & O. A. Malafeyev, 2018. "Corruption and botnet defense: a mean field game approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 977-999, September.
    2. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    3. Damien Besancenot & Habib Dogguy, 2015. "Paradigm Shift: A Mean Field Game Approach," Bulletin of Economic Research, Wiley Blackwell, vol. 67(3), pages 289-302, July.
    4. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    5. V. N. Kolokoltsov & O. A. Malafeyev, 2017. "Mean-Field-Game Model of Corruption," Dynamic Games and Applications, Springer, vol. 7(1), pages 34-47, March.
    6. Berenice Anne Neumann, 2020. "Stationary Equilibria of Mean Field Games with Finite State and Action Space," Dynamic Games and Applications, Springer, vol. 10(4), pages 845-871, December.
    7. René Carmona & Peiqi Wang, 2021. "A Probabilistic Approach to Extended Finite State Mean Field Games," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 471-502, May.
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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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