The cycles approach
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rodrigues-Neto, José Alvaro, 2012.
"The cycles approach,"
Journal of Mathematical Economics,
Elsevier, vol. 48(4), pages 207-211.
- Hellman, Ziv & Samet, Dov, 2012.
"How common are common priors?,"
Games and Economic Behavior,
Elsevier, vol. 74(2), pages 517-525.
- John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
- Barton L. Lipman, 2003.
"Finite Order Implications of Common Priors,"
Econometric Society, vol. 71(4), pages 1255-1267, 07.
- Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
- Jakub Steiner & Colin Stewart, 2010.
"Communication, Timing, and Common Learning,"
tecipa-389, University of Toronto, Department of Economics.
- Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007.
"Learning and Disagreement in an Uncertain World,"
Carlo Alberto Notebooks
48, Collegio Carlo Alberto.
- Milgrom, Paul & Stokey, Nancy, 1982.
"Information, trade and common knowledge,"
Journal of Economic Theory,
Elsevier, vol. 26(1), pages 17-27, February.
- Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
- Dov Samet, 1997.
"Common Priors and Separation of Convex Sets,"
Game Theory and Information
- Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
- John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- Hellwig, Martin F., 2013.
"From posteriors to priors via cycles: An addendum,"
Elsevier, vol. 118(3), pages 455-458.
- 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.
- Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
- Barelli, Paulo, 2009. "Consistency of beliefs and epistemic conditions for Nash and correlated equilibria," Games and Economic Behavior, Elsevier, vol. 67(2), pages 363-375, November.
- Ng, Man-Chung, 2003. "On the duality between prior beliefs and trading demands," Journal of Economic Theory, Elsevier, vol. 109(1), pages 39-51, March.
- Alfredo Di Tillio, 2002. "Iterated Expectations with Common Beliefs," Game Theory and Information 0209004, EconWPA.
- Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:207-211. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.