The Cycles Approach
The cycles approach uses graph theory and linear algebra to study models of knowledge, 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. If the cyclomatic number is zero, a common prior always exists, regardless of the probabilistic information given by players.posteriors. There is an isomorphism taking cycles into cycle equations; adding cycles is the counterpart of multiplying the corresponding cycle equations. With these tools, we study the processes of learning and forgetting, as well as properties of sub models (i.e., restricting attention to a proper subset of players), and decompositions of the set of players in subsets. We analyze how individual learning translates into more common knowledge or cycle destruction.
|Date of creation:||Jul 2011|
|Date of revision:|
|Contact details of provider:|| Postal: Canberra, ACT 2601|
Phone: +61 2 6125 3807
Fax: +61 2 6125 0744
Web page: http://rse.anu.edu.au/
More information through EDIRC
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.:
- 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.
- John Geanakoplos & Heracles M. Polemarchakis, 1982.
"We Can't Disagree Forever,"
Cowles Foundation Discussion Papers
639, Cowles Foundation for Research in Economics, Yale University.
- Steiner, Jakub & Stewart, Colin, 2011.
"Communication, timing, and common learning,"
Journal of Economic Theory,
Elsevier, vol. 146(1), pages 230-247, January.
- Jakub Steiner & Colin Stewart, 2010. "Communication, Timing, and Common Learning," Discussion Papers 1484, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jakub Steiner & Colin Stewart, 2010. "Communication, Timing, and Common Learning," Working Papers tecipa-389, University of Toronto, Department of Economics.
- Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
- Alfredo Di Tillio, 2002. "Iterated Expectations with Common Beliefs," Game Theory and Information 0209004, EconWPA.
- 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.
- Paul Milgrom & Nancy L.Stokey, 1979.
"Information, Trade, and Common Knowledge,"
377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
- Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
- Dov Samet, 1997.
"Common Priors and Separation of Convex Sets,"
Game Theory and Information
- 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.
- Ziv Hellman & Dov Samet, 2010.
"How Common Are Common Priors?,"
Discussion Paper Series
dp532, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006.
"Learning and Disagreement in an Uncertain World,"
NBER Working Papers
12648, National Bureau of Economic Research, Inc.
- 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.
- Rodrigues-Neto, José Alvaro, 2012.
"The cycles approach,"
Journal of Mathematical Economics,
Elsevier, vol. 48(4), pages 207-211.
- Barton L. Lipman, 1997.
"Finite Order Implications of Common Priors,"
Game Theory and Information
- Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
- 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.
- John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
When requesting a correction, please mention this item's handle: RePEc:acb:cbeeco:2011-547. 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: ()
If references are entirely missing, you can add them using this form.