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Beliefs in Network Games (Replaced by CentER DP 2008-05)

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  • Kets, W.

    (Tilburg University, Center for Economic Research)

Abstract

Networks can have an important effect on economic outcomes. Given the complexity of many of these networks, agents will generally not know their structure. We study the sensitivity of game-theoretical predictions to the specification of players’ (common) prior on the network in a setting where players play a fixed game with their neighbors and only have local information on the network structure. We show that two priors are close in a strategic sense if and only if (1) the priors assign similar probabilities to all events that involve a player and his neighbors, and (2) with high probability, a player believes, given his type, that his neighbors’ conditional beliefs are similar, and that his neighbors believe, given their type, that. . . the conditional beliefs of their neighbors are similar, for any number of iterations. Also, we show that the common but unrealistic assumptions that the size of the network is common knowledge or that the types of players are independent are far from innocuous: if these assumptions are violated, small probability events can have a large effect on outcomes through players’ conditional beliefs.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-46.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200746

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

Related research

Keywords: Network games; incomplete information; higher order beliefs; continuity; random networks; population uncertainty;

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  1. Marcel Fafchamps & Susan Lund, . "Risk Sharing Networks in Rural Philippines," Working Papers 97014, Stanford University, Department of Economics.
  2. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
  3. Conley, T.G. & Udry, C.R., 2000. "Learning about a New Technology: Pineapple in Ghana," Papers 817, Yale - Economic Growth Center.
  4. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Stephen Morris, . "Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching," Penn CARESS Working Papers 1879bf5487d743edef7f32bb2, Penn Economics Department.
  7. Rothschild, Casey G., 2005. "Payoff continuity in incomplete information games: a comment," Journal of Economic Theory, Elsevier, vol. 120(2), pages 270-274, February.
  8. George J. mailath & Larry Samuelson & Avner Shaked, . "Correlated Equilibria and Local Interactions," ELSE working papers 030, ESRC Centre on Economics Learning and Social Evolution.
  9. Arun Sundararajan, 2004. "Local Network Effects and Network Structure," Industrial Organization 0412011, EconWPA.
  10. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
  11. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  12. 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.
  13. Kets, W., 2007. "Convergence of Beliefs in Bayesian Network Games," Discussion Paper 2007-98, Tilburg University, Center for Economic Research.
  14. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
  15. 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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