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Cycles of length two in monotonic models

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  • José Alvaro Rodrigues-Neto

Abstract

In the context of partitional knowledge models, we prove that, in a monotonic model, any cycle equation can be obtained as the product of cycle equations corresponding to cycles of length two. Hence, if a model is monotonic, has finite states, and players' posteriors satisfy all cycle equations corresponding to cycles of length two, then these posteriors are consistent (i.e., there is a common prior). We also propose a new and elegant proof for one of the main results of Rodrigues-Neto 2012.

Suggested Citation

  • 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.
    • Handle: RePEc:acb:cbeeco:2012-587
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp587.pdf
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    References listed on IDEAS

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    1. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    2. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    3. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
    4. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    5. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    6. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    7. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    8. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.
    9. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    10. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
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    Cited by:

    1. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    2. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.

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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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