Constrained public goods in networks
23 May 2018
by Nizar Allouch, University of Kent, and Maia King, University of Oxford. Discussion paper KDPE 1806, May 2018.
Voluntary contributions account for the provision of many public goods, ranging from essential infrastructure, education, to health care, while at the aggregate level charitable giving represents a significant proportion of GDP in many countries. The seminal contribution of Bergstrom, Blume, and Varian (1986), built on an earlier striking result by Warr (1981), provides a rigorous investigation of the standard model of private provision of pure public goods.
Recent work on public goods in networks, initiated by the key paper of Bramoullé and Kranton (2007), has many interesting facets and applications. The technology of network analysis allows us to generalise from the provision of pure public goods, which benefit all agents, to a more detailed model of local public goods with a heterogeneous benefit structure shaped by a network.
This paper analyses the private provision of public goods where agents interact within a fixed network structure and may benefit only from their direct neighbours’ provisions. We survey the literature and then generalise the public goods in networks model of Bramoullé and Kranton (2007) to allow for constrained provision. In so doing, we show that, any network supports a Nash equilibrium with no intermediate contributors.
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