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.
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- 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.
- 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.
- John Geanakoplos & Heracles M. Polemarchakis, 1982.
"We Can't Disagree Forever,"
Cowles Foundation Discussion Papers
639, Cowles Foundation for Research in Economics, Yale University.
- John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
- 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.
- Dov Samet, 1997.
"Common Priors and Separation of Convex Sets,"
Game Theory and Information
- 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.
- Alfredo Di Tillio, 2002. "Iterated Expectations with Common Beliefs," Game Theory and Information 0209004, EconWPA.
- Jakub Steiner & Colin Stewart, 2010.
"Communication, Timing, and Common Learning,"
1484, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- Jose Alvaro Rodrigues-Neto, 2011.
"The Cycles Approach,"
ANU Working Papers in Economics and Econometrics
2011-547, Australian National University, College of Business and Economics, School of Economics.
- Hellman, Ziv & Samet, Dov, 2012.
"How common are common priors?,"
Games and Economic Behavior,
Elsevier, vol. 74(2), pages 517-525.
- Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006.
"Learning and Disagreement in an Uncertain World,"
NBER Working Papers
12648, National Bureau of Economic Research, Inc.
- Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
- 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.
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