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Equilibrium Existence and Uniqueness In Network Games with Additive Preferences

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  • Yann Rébillé

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

  • Lionel Richefort

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

Abstract

A directed network game of imperfect strategic substitutes with heterogeneous players is analyzed. We consider concave additive separable utility functions that encompass the quasi-linear ones. It is found that pure strategy Nash equilibria verify a non-linear complementarity problem. By requiring appropriate concavity in the utility functions, the existence of an equilibrium point is shown and equilibrium uniqueness is established with a P -matrix. Then, it appears that previous findings on network structure and sparsity hold for many more games.

Suggested Citation

  • Yann Rébillé & Lionel Richefort, 2012. "Equilibrium Existence and Uniqueness In Network Games with Additive Preferences," Working Papers hal-00732962, HAL.
    • Handle: RePEc:hal:wpaper:hal-00732962
    DOI: 10.1016/j.ejor.2013.07.014
    Note: View the original document on HAL open archive server: https://hal.science/hal-00732962v1
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    Cited by:

    1. Rébillé, Yann & Richefort, Lionel, "undated". "Networks of Many Public Goods with Non-Linear Best Replies," Climate Change and Sustainable Development 206421, Fondazione Eni Enrico Mattei (FEEM).
    2. 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.
    3. Yann Rébillé & Lionel Richefort, 2015. "Influence and Social Tragedy in Networks," Revue d'économie politique, Dalloz, vol. 125(6), pages 811-833.
    4. Bervoets, Sebastian & Makihara, Kohmei, 2025. "Public goods in networks: Comparative statics results," Journal of Economic Theory, Elsevier, vol. 228(C).
    5. Zhao, Wenna & Ma, Kai & Yang, Jie & Guo, Shiliang, 2024. "A multi-time scale demand response scheme based on noncooperative game for economic operation of industrial park," Energy, Elsevier, vol. 302(C).

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