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Equilibrium Existence and Uniqueness In Network Games with Additive Preferences

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Author Info

  • Yann Rébillé

    ()
    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - Université de Nantes : EA4272)

  • Lionel Richefort

    ()
    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - Université de Nantes : EA4272)

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.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00732962.

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Date of creation: 17 Sep 2012
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Handle: RePEc:hal:wpaper:hal-00732962

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

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References

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  1. Nizar Allouch, 2012. "On the Private Provision of Public Goods on Networks," Working Papers 2012.40, Fondazione Eni Enrico Mattei.
  2. B. Curtis Eaton, 2004. "The elementary economics of social dilemmas," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 805-829, November.
  3. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2004. "Who's Who in Networks. Wanted: The Key Player," Working Papers 178, Barcelona Graduate School of Economics.
  4. Yann Rébillé & Lionel Richefort, 2012. "Sharing Water from many Rivers," Working Papers hal-00678997, HAL.
  5. Ballester, Coralio & Calvó-Armengol, Antoni, 2010. "Interactions with hidden complementarities," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 397-406, November.
  6. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2008. "Network Games," Economics Working Papers ECO2008/07, European University Institute.
    • 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.
  7. 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.
  8. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
  9. AMBEC, Steve & SPRUMONT, Yves, 2000. "Sharing a River," Cahiers de recherche 2000-08, Universite de Montreal, Departement de sciences economiques.
  10. 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.
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Cited by:
  1. Yann Rébillé & Lionel Richefort, 2014. "Influence and Social Tragedy in Networks," Working Papers hal-00924017, HAL.

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