Networks of Many Public Goods with Non-Linear Best Replies

31 Pages Posted: 17 Jun 2015

See all articles by Yann Rébillé

Yann Rébillé

University of Nantes

Lionel Richefort

Institut d’Economie et de Management de Nantes

Date Written: June 17, 2015

Abstract

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.

Keywords: Bipartite Graph, Public Good, Nash Equilibrium, Non-Linear, Complementarity Problem

JEL Classification: C72, D85, H41

Suggested Citation

Rébillé, Yann and Richefort, Lionel, Networks of Many Public Goods with Non-Linear Best Replies (June 17, 2015). FEEM Working Paper No. 057.2015, Available at SSRN: https://ssrn.com/abstract=2619558 or http://dx.doi.org/10.2139/ssrn.2619558

Yann Rébillé

University of Nantes ( email )

1, quai de Tourville BP
Nantes Cedex 1
Nantes, 44313
France

Lionel Richefort (Contact Author)

Institut d’Economie et de Management de Nantes ( email )

Chemin de la Censive du Tertre, BP 52231
Nantes Cedex 3, 44322
France

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