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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

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 are the complex computations necessary to determine dynamic mean-field equilibria, which make it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards stationary equilibria with deterministic equilibrium strategies under rather broad conditions. Moreover, for a two-strategy setting, we also obtain a global convergence result under stronger, yet intuitive conditions.

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  • Berenice Anne Neumann, 2020. "A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space," Papers 2008.13420, arXiv.org.
    • Handle: RePEc:arx:papers:2008.13420
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. 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.
    3. 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.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    5. repec:hal:cepnwp:halshs-00590527 is not listed on IDEAS
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    1. Neumann, Berenice Anne, 2022. "Essential stationary equilibria of mean field games with finite state and action space," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 85-91.

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