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Best-response dynamics in directed network games

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  • Kozics, György
  • Szöke, Nora Gabriella
  • Bayer, Péter

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

  • Kozics, György & Szöke, Nora Gabriella & Bayer, Péter, 2022. "Best-response dynamics in directed network games," TSE Working Papers 22-1290, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:126505
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    Cited by:

    1. Bervoets, Sebastian & Faure, Mathieu, 2020. "Convergence in games with continua of equilibria," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 25-30.
    2. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).

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    More about this item

    Keywords

    Networks; externalities; local public goods; potential games; non-reciprocal relations;
    All these keywords.

    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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