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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 - UN - Université de Nantes)

  • Lionel Richefort

    () (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - 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
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00732962
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    References listed on IDEAS

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    1. 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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    5. Yann Rébillé & Lionel Richefort, 2012. "Sharing Water from many Rivers," Working Papers hal-00678997, HAL.
    6. B. Curtis Eaton, 2004. "The elementary economics of social dilemmas," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 805-829, November.
    7. 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.
    8. Wang, Qinan & Parlar, Mahmut, 1989. "Static game theory models and their applications in management science," European Journal of Operational Research, Elsevier, vol. 42(1), pages 1-21, September.
    9. Ballester, Coralio & Calvó-Armengol, Antoni, 2010. "Interactions with hidden complementarities," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 397-406, November.
    10. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 218-244.
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    Cited by:

    1. Yann Rébillé & Lionel Richefort, 2014. "Networks of many public goods with non-linear best replies," Working Papers hal-01074708, HAL.
    2. Yann Rébillé & Lionel Richefort, 2015. "Influence and Social Tragedy in Networks," Revue d'économie politique, Dalloz, vol. 125(6), pages 811-833.
    3. Lionel Richefort, 2017. "Warm-Glow Giving in Networks with Multiple Public Goods," Working Papers 2017.32, Fondazione Eni Enrico Mattei.

    More about this item

    Keywords

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

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