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The cycles approach

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  • Rodrigues-Neto, José Alvaro

Abstract

The cycles approach uses linear algebra, graph theory, and probability theory to study common prior existence and analyze models of knowledge, which are characterized by a state space, a set of players, and their partitions. In finite state spaces, there is a simple formula for the cyclomatic number, i.e., the dimension of cycle spaces of a model. We prove that the cyclomatic number is the minimum number of cycle equations that must be checked to guarantee the existence of a common prior, and explain why some cycle equations are automatically satisfied. There is an isomorphism taking cycles into cycle equations; adding cycles is the counterpart of multiplying the corresponding cycle equations. If the cyclomatic number is zero, a common prior always exists, regardless of the probabilistic information given by players’ posteriors.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 4 ()
Pages: 207-211

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Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:207-211

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Consistency; Cycle; Cyclomatic; Prior; Posterior;

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References

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  7. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
  8. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
  9. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
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  15. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
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  18. Jakub Steiner & Colin Stewart, 2010. "Communication, Timing, and Common Learning," Working Papers tecipa-389, University of Toronto, Department of Economics.
  19. José Alvaro Rodrigues-Neto, 2012. "Cycles of length two in monotonic models," ANU Working Papers in Economics and Econometrics 2012-587, Australian National University, College of Business and Economics, School of Economics.
  20. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
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Cited by:
  1. Martin Hellwig, 2011. "From Posteriors to Priors via Cycles: An Addendum," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2011_07, Max Planck Institute for Research on Collective Goods.
  2. José Alvaro Rodrigues-Neto, 2012. "Monotonic models and cycles," ANU Working Papers in Economics and Econometrics 2012-586, Australian National University, College of Business and Economics, School of Economics.
  3. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
  4. José Alvaro Rodrigues-Neto, 2012. "Cycles of length two in monotonic models," ANU Working Papers in Economics and Econometrics 2012-587, Australian National University, College of Business and Economics, School of Economics.

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