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The Evolution of Networks and Local Public Good Provision: A Potential Approach

by 1,† and 2,*,†
1
Departamento de Economía, Edificio Amigos, Universidad de Navarra, 31009 Pamplona, Spain
2
Department of Economics, University of Antwerp, Prinsstraat 13, 2000 Antwerp, Belgium
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Paolo Pin and Ulrich Berger
Received: 4 June 2021 / Revised: 24 June 2021 / Accepted: 29 June 2021 / Published: 2 July 2021
(This article belongs to the Special Issue Game Theory in Social Networks)
In this paper, we propose a game in which each player decides with whom to establish a costly connection and how much local public good is provided when benefits are shared among neighbors. We show that, when agents are homogeneous, Nash equilibrium networks are nested split graphs. Additionally, we show that the game is a potential game, even when we introduce heterogeneity along several dimensions. Using this result, we introduce stochastic best reply dynamics and show that this admits a unique and stationary steady state distribution expressed in terms of the potential function of the game. Hence, even if the set of Nash equilibria is potentially very large, the long run predictions are sharp. View Full-Text
Keywords: network formation; network games; public goods; potential games network formation; network games; public goods; potential games
MDPI and ACS Style

Kinateder, M.; Merlino, L.P. The Evolution of Networks and Local Public Good Provision: A Potential Approach. Games 2021, 12, 55. https://0-doi-org.brum.beds.ac.uk/10.3390/g12030055

AMA Style

Kinateder M, Merlino LP. The Evolution of Networks and Local Public Good Provision: A Potential Approach. Games. 2021; 12(3):55. https://0-doi-org.brum.beds.ac.uk/10.3390/g12030055

Chicago/Turabian Style

Kinateder, Markus, and Luca P. Merlino 2021. "The Evolution of Networks and Local Public Good Provision: A Potential Approach" Games 12, no. 3: 55. https://0-doi-org.brum.beds.ac.uk/10.3390/g12030055

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