The evolution of networks and local public good provision: a potential approach
Keywords: 
Network formation
Network games
Public goods
Potential games
Issue Date: 
2021
Publisher: 
MPDI
ISSN: 
2073-4336
Note: 
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license
Citation: 
Kinateder, M.; Merlino, L.P. The Evolution of Networks and Local Public Good Provision: A Potential Approach. Games 2021, 12, 55
Abstract
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.

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