FEEM working papers "Note di lavoro" series
2012 .040

On the Private Provision of Public Goods on Networks


Authors: Nizar Allouch
Series: Climate Change and Sustainable Development
Editor: Carlo Carraro
Keywords: Public Goods, Uniqueness Of Nash Equilibrium, Network Games, Neutrality, Bonacich Centrality, Main Eigenvalue
JEL n.: C72, D31, H41

Abstract

This paper analyzes the private provision of public goods where consumers interact within a  fixed network structure and may benefit only from their direct neighbors’ provisions. We present a proof for existence and uniqueness of a Nash equilibrium with general best-reply functions. Our uniqueness result simultaneously extends similar results in Bergstrom, Blume, and Varian (1986) on the private provision of public goods to networks and Bramoullé, Kranton, and D'Amours (2011) on games of strategic substitutes to nonlinear best-reply functions. In addition, we investigate the neutrality result of Warr (1983) and Bergstrom, Blume, and Varian (1986) whereby consumers are able to offset income redistributions and tax-financed government contributions. To this effect, we establish that the neutrality result has a limited scope of application beyond regular networks.

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