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Networks of Many Public Goods with Non-Linear Best Replies

Author

Listed:
  • Yann Rébillé

    (LEMNA, Université de Nantes)

  • Lionel Richefort

    (LEMNA, Université de Nantes)

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.

Suggested Citation

  • Yann Rébillé & Lionel Richefort, 2015. "Networks of Many Public Goods with Non-Linear Best Replies," Working Papers 2015.57, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2015.57
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    References listed on IDEAS

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    1. R. C. Cornes & A. G. Schweinberger, 1996. "Free Riding and the Inefficiency of the Private Production of Pure Public Goods," Canadian Journal of Economics, Canadian Economics Association, vol. 29(1), pages 70-91, February.
    2. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
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    5. Rébillé, Yann & Richefort, Lionel, 2014. "Equilibrium existence and uniqueness in network games with additive preferences," European Journal of Operational Research, Elsevier, vol. 232(3), pages 601-606.
    6. Ballester, Coralio & Calvó-Armengol, Antoni, 2010. "Interactions with hidden complementarities," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 397-406, November.
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    9. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
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    Cited by:

    1. Lionel Richefort, 2018. "Warm-glow giving in networks with multiple public goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1211-1238, November.

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    More about this item

    Keywords

    Bipartite Graph; Public Good; Nash Equilibrium; Non-Linear; Complementarity Problem;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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