Provision of Public Goods on Networks: On Existence, Uniqueness, and Centralities

TL;DR

This paper analyzes how network structure influences the existence, uniqueness, and efficiency of public goods provision among strategic agents, linking efforts to network centralities and uncovering effects of network walks.

Contribution

It provides necessary and sufficient conditions for Nash equilibrium uniqueness and existence, unifies existing results, and links efforts to agents' centralities in the network.

Findings

Unique Nash equilibrium conditions depend on network structure

Efforts at equilibrium relate to agents' centrality measures

Network walk lengths influence effort distribution effects

Abstract

We consider the provision of public goods on networks of strategic agents. We study different effort outcomes of these network games, namely, the Nash equilibria, Pareto efficient effort profiles, and semi-cooperative equilibria (effort profiles resulting from interactions among coalitions of agents). We identify necessary and sufficient conditions on the structure of the network for the uniqueness of the Nash equilibrium. We show that our finding unifies (and strengthens) existing results in the literature. We also identify conditions for the existence of Nash equilibria for the subclasses of games at the two extremes of our model, namely games of strategic complements and games of strategic substitutes. We provide a graph-theoretical interpretation of agents' efforts at the Nash equilibrium, as well as the Pareto efficient outcomes and semi-cooperative equilibria, by linking an agent's decision to her centrality in the interaction network. Using this connection, we separate the effects of incoming and outgoing edges on agents' efforts and uncover an alternating effect over walks of different length in the network.