No. 689: On the Private Provision of Public Goods on Networks
Nizar Allouch ,
Queen Mary, University of London
February 1, 2012
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.
J.E.L classification codes: C72, D31, H41
Keywords:Public goods, Uniqueness of Nash equilibrium, Network games, Neutrality, Bonacich centrality, Main eigenvalue