Monotonic models and cycles
A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posterior beliefs for the players is consistent (i.e., there is a common prior). We describe the lattice properties of monotonic models, develop a test to check if a model is monotonic, propose a simple sufficient condition for non-monotonicity, and provide some examples. We also study models having circular orders, a weakening of monotonicity.
|Date of creation:||Oct 2012|
|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
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.:
- Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
- 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.
- 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.
- Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
- Dov Samet, 1997.
"Common Priors and Separation of Convex Sets,"
Game Theory and Information
- Rodrigues-Neto, José Alvaro, 2012.
"The cycles approach,"
Journal of Mathematical Economics,
Elsevier, vol. 48(4), pages 207-211.
- Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
- Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
- Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
- Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
- 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.
When requesting a correction, please mention this item's handle: RePEc:acb:cbeeco:2012-586. 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.