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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-00732962
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    References listed on IDEAS

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    1. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    2. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
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    8. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 218-244.
    9. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    10. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    11. Yann Rébillé & Lionel Richefort, 2012. "Sharing Water from many Rivers," Working Papers hal-00678997, HAL.
    12. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    13. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
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    Cited by:

    1. Yann Rébillé & Lionel Richefort, 2015. "Influence and Social Tragedy in Networks," Revue d'économie politique, Dalloz, vol. 125(6), pages 811-833.
    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, 2014. "Networks of many public goods with non-linear best replies," Working Papers hal-01074708, HAL.

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    Keywords

    P -matrix; network game; additive preferences; complementarity problem;
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