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The cycles approach

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  • Rodrigues-Neto, José Alvaro

Abstract

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.

Suggested Citation

  • Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:207-211
    DOI: 10.1016/j.jmateco.2012.05.002
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    References listed on IDEAS

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    Cited by:

    1. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    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.
    3. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    4. repec:eee:matsoc:v:87:y:2017:i:c:p:11-21 is not listed on IDEAS
    5. Luciana C. Fiorini & José A. Rodrigues-Neto, 2014. "Self-Consistency and Common Prior in Non-Partitional Knowledge Models," ANU Working Papers in Economics and Econometrics 2014-621, Australian National University, College of Business and Economics, School of Economics.
    6. 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.

    More about this item

    Keywords

    Consistency; Cycle; Cyclomatic; Prior; Posterior;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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