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We model a bipartite network in which links connect agents with public goods. Agents play a voluntary contribution game in which they decide how much to contribute to each public good they are connected to. We show that the problem of finding a Nash equilibrium can be posed as a non-linear complementarity one. The existence of an equilibrium point is established for a wide class of individual preferences. We then find a simple sufficient condition, on network structure only, that guarantees the uniqueness of the equilibria, and provide an easy procedure for building networks that respects this condition.
Rébillé, Yann and Richefort, Lionel, "Networks of Many Public Goods with Non-Linear Best Replies" (June 17, 2015). Fondazione Eni Enrico Mattei Working Papers. Paper 991.