Best-response dynamics in directed network games

Peter Bayer, György Kozics and Nora Gabriella Szöke

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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)
Date: 2022-01
New Economics Papers: this item is included in nep-gth, nep-mic and nep-net
Note: View the original document on HAL open archive server: https://hal.science/hal-03542533v1
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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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