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Equilibrium existence and uniqueness in network games with additive preferences

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  • Rébillé, Yann
  • Richefort, Lionel

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. For this reason, it appears that previous findings on network structure and sparsity hold for many more games.

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  • 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.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:3:p:601-606
    DOI: 10.1016/j.ejor.2013.07.014
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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.
    3. Ambec, Stefan & Sprumont, Yves, 2002. "Sharing a River," Journal of Economic Theory, Elsevier, vol. 107(2), pages 453-462, December.
    4. Francis Bloch & Unal Zenginobuz, 2007. "The effect of spillovers on the provision of local public goods," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 199-216, November.
    5. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    6. Yann Rébillé & Lionel Richefort, 2012. "Sharing Water from many Rivers," Working Papers hal-00678997, HAL.
    7. B. Curtis Eaton, 2004. "The elementary economics of social dilemmas," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 805-829, November.
    8. 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.
    9. 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.
    10. Ballester, Coralio & Calvó-Armengol, Antoni, 2010. "Interactions with hidden complementarities," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 397-406, November.
    11. 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.
    12. 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.
    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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