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Convergence of Beliefs in Bayesian Network Games

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  • Kets, W.

    (Tilburg University, Center for Economic Research)

Abstract

In many contexts, players interact only with a subset of the whole population, i.e., players interact on a network. This paper a setting in which players are located on a network and play a fixed game with their neighbors. Players have incomplete information on the network structure. They have a common prior over the network, and in addition, they know the number of connections they have. That is, their type is their degree. We study the sensitivity of game-theoretic predictions to the specification of players’ beliefs. We show that two priors are close in a strategic sense if and only if they assign similar probabilities to all local events, i.e., to all events involving the types of a player and his neighbors. This means that in order to fully explore the range of possible strategic outcomes, it suffices to vary the type distribution and the correlation among player types. On the other hand, it is not enough to vary only the type distribution, which has been the focus of much of the literature so far.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-98.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200798

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Web page: http://center.uvt.nl

Related research

Keywords: Network games; incomplete information; payoff continuity;

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References

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  1. 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.
  2. Timothy G. Conley & Christopher R. Udry, 2005. "Learning about a new technology: pineapple in Ghana," Proceedings, Federal Reserve Bank of San Francisco.
  3. Marcel Fafchamps & Susan Lund, 2000. "Risk-Sharing Networks in Rural Philippines," Economics Series Working Papers 10, University of Oxford, Department of Economics.
  4. Matthew O. Jackson & Leeat Yariv, 2007. "Diffusion of Behavior and Equilibrium Properties in Network Games," American Economic Review, American Economic Association, vol. 97(2), pages 92-98, May.
  5. Engl Greg, 1995. "Lower Hemicontinuity of the Nash Equilibrium Correspondence," Games and Economic Behavior, Elsevier, vol. 9(2), pages 151-160, May.
  6. Dunia López-Pintado, 2006. "Contagion and coordination in random networks," International Journal of Game Theory, Springer, vol. 34(3), pages 371-381, October.
  7. Atsushi Kajii & Stephen Morris, 1997. "Payoff Continuity in Incomplete Information Games," Discussion Papers 1193R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Arun Sundararajan, 2004. "Local Network Effects and Network Structure," Industrial Organization 0412011, EconWPA.
  10. Goolsbee, Austan & Klenow, Peter J, 2002. "Evidence on Learning and Network Externalities in the Diffusion of Home Computers," Journal of Law and Economics, University of Chicago Press, vol. 45(2), pages 317-43, October.
  11. Galeotti, Andrea & Vega-Redondo, Fernando, 2005. "Strategic analysis in complex networks with local externalities," Working Papers 1224, California Institute of Technology, Division of the Humanities and Social Sciences.
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Cited by:
  1. Kets, W., 2007. "Beliefs in Network Games (Replaced by CentER DP 2008-05)," Discussion Paper 2007-46, Tilburg University, Center for Economic Research.

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