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Interactions with hidden complementarities

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  • Ballester, Coralio
  • Calvó-Armengol, Antoni

Abstract

We consider a finite population simultaneous move game with heterogeneous interaction modes across different pairs of players. We allow for general interaction patterns, but restrict our analysis to games whose pure strategy Nash equilibrium conditions boil down to a set of piece-wise linear conditions, so that an equilibrium is a solution to a linear complementarity problem. We introduce a new class of games for which a suitable linear transformation of the original interaction matrix induces a game with complementarities. We provide general moderation conditions on the interaction matrix such that a game in this class has a unique Nash equilibrium, that we are able to characterize by means of a closed-form expression involving a generalized version of the Katz network measure of node centrality.

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Bibliographic Info

Article provided by Elsevier in its journal Regional Science and Urban Economics.

Volume (Year): 40 (2010)
Issue (Month): 6 (November)
Pages: 397-406

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Handle: RePEc:eee:regeco:v:40:y:2010:i:6:p:397-406

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Keywords: Nash equilibrium Uniqueness Complementarity Moderation Interaction matrix Linear complementarity problem;

References

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  1. 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.
  2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  3. George J. Borjas, 1997. "To Ghetto or Not to Ghetto: Ethnicity and Residential Segregation," NBER Working Papers 6176, National Bureau of Economic Research, Inc.
  4. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
  5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  6. Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2009. "Delinquent Networks," CEPR Discussion Papers 7293, C.E.P.R. Discussion Papers.
  7. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
  8. Bamon, Rodrigo & Fraysse, Jean, 1985. "Existence of Cournot Equilibrium in Large Markets," Econometrica, Econometric Society, vol. 53(3), pages 587-97, May.
  9. Kolstad, Charles D & Mathiesen, Lars, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 681-90, October.
  10. Antoni Calvó-Armengol & Joan de Martí, 2007. "Communication Networks: Knowledge and Decisions," American Economic Review, American Economic Association, vol. 97(2), pages 86-91, May.
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Citations

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Cited by:
  1. Yann Rébillé & Lionel Richefort, 2012. "Equilibrium Existence and Uniqueness In Network Games with Additive Preferences," Working Papers hal-00732962, HAL.
  2. Mohamed Belhaj & Sebastian Bervoets & Frédéric Deroïan, 2013. "Network Design under Local Complementarities," Working Papers halshs-00796487, HAL.
  3. Junjie Zhou & Ying-Ju Chen, 2013. "Targeted information release in social networks," Working Papers 13-04, NET Institute.
  4. Bloch, Francis & Quérou, Nicolas, 2013. "Pricing in social networks," Games and Economic Behavior, Elsevier, vol. 80(C), pages 243-261.
  5. Hernández, Penélope & Muñoz-Herrera, Manuel & Sánchez, Ángel, 2013. "Heterogeneous network games: Conflicting preferences," Games and Economic Behavior, Elsevier, vol. 79(C), pages 56-66.
  6. Mohamed Belhaj & Yann Bramoullé & Frédéric Deroian, 2012. "Network Games under Strategic Complementarities," AMSE Working Papers 1225, Aix-Marseille School of Economics, Marseille, France.
  7. Mohamed Belhaj & Sebastian Bervoets & Frédéric Deroïan, 2013. "Network Design under Local Complementarities," AMSE Working Papers 1309, Aix-Marseille School of Economics, Marseille, France, revised 12 Feb 2013.
  8. Belhaj, Mohamed & Deroïan, Frédéric, 2012. "Risk taking under heterogenous revenue sharing," Journal of Development Economics, Elsevier, vol. 98(2), pages 192-202.
  9. Belhaj, Mohamed & Deroïan, Frédéric, 2013. "Strategic interaction and aggregate incentives," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 183-188.

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