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

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

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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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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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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private 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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  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. 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. [Downloadable!] (restricted)
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  4. 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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  5. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May. [Downloadable!] (restricted)
  6. 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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  7. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer, vol. 27(3), pages 375-392. [Downloadable!] (restricted)
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  8. Rothschild, Casey G., 2005. "Payoff continuity in incomplete information games: a comment," Journal of Economic Theory, Elsevier, vol. 120(2), pages 270-274, February. [Downloadable!] (restricted)
  9. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November. [Downloadable!] (restricted)
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  10. Arun Sundararajan, 2004. "Local Network Effects and Network Structure," Industrial Organization 0412011, EconWPA. [Downloadable!]
  11. 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. [Downloadable!]
  12. Avner Shaked & Larry Samuelson & George J. Mailath, 1997. "Correlated equilibria and local interactions (*)," Economic Theory, Springer, vol. 9(3), pages 551-556.
  13. Kets, W., 2007. "Convergence of Beliefs in Bayesian Network Games," Discussion Paper 2007-98, Tilburg University, Center for Economic Research. [Downloadable!]
  14. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June. [Downloadable!] (restricted)
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