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Best-response dynamics in directed network games

Author

Listed:
  • Peter Bayer

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • György Kozics
  • Nora Gabriella Szöke

Abstract

We study public goods games played on networks with possibly non-recip-rocal relationships between players. Examples for this type of interactions include one-sided relationships, mutual but unequal relationships, and par-asitism. It is well known that many simple learning processes converge to a Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. However, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices and quadratic best-response potentials. Additionally, we show convergence in a second class of networks; those rescalable into networks with weak exter-nalities. We characterize the latter class by the spectral properties of the absolute value of the network's weight matrix and by another best-response potential structure.

Suggested Citation

  • Peter Bayer & György Kozics & Nora Gabriella Szöke, 2022. "Best-response dynamics in directed network games," Working Papers hal-03542533, HAL.
    • Handle: RePEc:hal:wpaper:hal-03542533
    Note: View the original document on HAL open archive server: https://hal.science/hal-03542533v1
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    References listed on IDEAS

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    2. Argyrios Deligkas & Gregory Gutin & Mark Jones & Philip R. Neary & Anders Yeo, 2025. "Public Goods Games in Directed Networks with Constraints on Sharing," Papers 2511.11475, arXiv.org.
    3. Bervoets, Sebastian & Faure, Mathieu, 2020. "Convergence in games with continua of equilibria," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 25-30.
    4. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    5. Cao, Zhigang & Li, Guopeng & Shen, Sixian & Zhu, Feng, 2025. "Potentials in quadratic Cournot cross-holding games," Journal of Mathematical Economics, Elsevier, vol. 119(C).
    6. Yukun Cheng & Xiaotie Deng & Yunxuan Ma, 2025. "Networked Digital Public Goods Games with Heterogeneous Players and Convex Costs," Papers 2502.01001, arXiv.org.
    7. Daeyoung Jeong & Tongseok Lim & Euncheol Shin, 2024. "Robust Intervention in Networks," Papers 2501.00235, arXiv.org, revised Feb 2025.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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