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Convergence of Beliefs in Bayesian Network Games

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Author Info
Kets, W. (Tilburg University, Center for Economic Research)

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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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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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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
Z13 - Other Special Topics - - Cultural Economics - - - Social Norms and Social Capital; Social Networks Economic Anthropology

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References listed on IDEAS
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  1. 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.
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  2. Timothy G. Conley & Christopher R. Udry, 2005. "Learning about a new technology: pineapple in Ghana," Proceedings, Federal Reserve Bank of San Francisco. [Downloadable!]
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  3. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September. [Downloadable!] (restricted)
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  4. Goolsbee, Austan & Klenow, Peter J, 2002. "Evidence on Learning and Network Externalities in the Diffusion of Home Computers," Journal of Law & Economics, University of Chicago Press, vol. 45(2), pages 317-43, October.
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  5. Fafchamps, Marcel & Lund, Susan, 2003. "Risk-sharing networks in rural Philippines," Journal of Development Economics, Elsevier, vol. 71(2), pages 261-287, August. [Downloadable!] (restricted)
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  6. Arun Sundararajan, 2004. "Local Network Effects and Network Structure," Industrial Organization 0412011, EconWPA. [Downloadable!]
  7. 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. [Downloadable!]
  8. Engl Greg, 1995. "Lower Hemicontinuity of the Nash Equilibrium Correspondence," Games and Economic Behavior, Elsevier, vol. 9(2), pages 151-160, May. [Downloadable!] (restricted)
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  1. Kets, W., 2007. "Beliefs in Network Games (Replaced by CentER DP 2008-05)," Discussion Paper 2007-46, Tilburg University, Center for Economic Research. [Downloadable!]
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