Best-response dynamics in directed network games

György Kozics, Nora Gabriella Szöke and Peter Bayer

No 22-1290, TSE Working Papers from Toulouse School of Economics (TSE)

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.

Keywords: Networks; externalities; local public goods; potential games; non-reciprocal relations (search for similar items in EconPapers)
JEL-codes: C72 D62 D85 (search for similar items in EconPapers)
Date: 2022-01-21
New Economics Papers: this item is included in nep-gth and nep-net
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Related works:
Journal Article: Best-response dynamics in directed network games (2023)
Working Paper: Best-response dynamics in directed network games (2023)
Working Paper: Best-response dynamics in directed network games (2022)
Working Paper: Best-Response Dynamics in Directed Network Games (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:126505

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