FEEM working papers "Note di lavoro" series
2015 .057

Networks of Many Public Goods with Non-Linear Best Replies

Authors: Yann Rébillé, Lionel Richefort
Series: Climate Change and Sustainable Development
Editor: Carlo Carraro
Keywords: Bipartite Graph, Public Good, Nash Equilibrium, Non-Linear, Complementarity Problem
JEL n.: C72, D85, H41


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.  

Suggested citation: Rébillé, Y., Richefort, L., 'Networks of Many Public Goods with Non-Linear Best Replies', Nota di Lavoro 57.2015, Milan, Italy: Fondazione Eni Enrico Mattei

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