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Strategic Interaction and Networks

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  • Yann Bramoullé
  • Rachel Kranton
  • Martin D'Amours

Abstract

This paper brings a general network analysis to a wide class of economic games. A network, or interaction matrix, tells who directly interacts with whom. A major challenge is determining how network structure shapes overall outcomes. We have a striking result. Equilibrium conditions depend on a single number: the lowest eigenvalue of a network matrix. Combining tools from potential games, optimization, and spectral graph theory, we study games with linear best replies and characterize the Nash and stable equilibria for any graph and for any impact of players’ actions. When the graph is sufficiently absorptive (as measured by this eigenvalue), there is a unique equilibrium. When it is less absorptive, stable equilibria always involve extreme play where some agents take no actions at all. This paper is the first to show the importance of this measure to social and economic outcomes, and we relate it to different network link patterns.

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File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2010/CIRPEE10-18.pdf
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Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 1018.

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Date of creation: 2010
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Handle: RePEc:lvl:lacicr:1018

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Related research

Keywords: Networks; potential games; lowest eigenvalue; stable equilibria; asymmetric equilibria;

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Cited by:
  1. Zenou, Yves & König, Michael D. & Tessone, Claudio J., 0. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society.
  2. Belhaj, Mohamed & Deroïan, Frédéric, 2012. "Risk taking under heterogenous revenue sharing," Journal of Development Economics, Elsevier, vol. 98(2), pages 192-202.
  3. Lorenzo Burlon, 2012. "How Do Aggregate Fluctuations Depend on the Network Structure of the Economy?," Working Papers in Economics 278, Universitat de Barcelona. Espai de Recerca en Economia.
  4. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
  5. Carlos Lever Guzmán, 2010. "Strategic Spending in Voting Competitions with Social Networks," Working Papers 2010-16, Banco de México.
  6. Marco Pelliccia, 2012. "Risk-sharing and probabilistic network structure," Birkbeck Working Papers in Economics and Finance 1214, Birkbeck, Department of Economics, Mathematics & Statistics.

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