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The cycles approach

  • Rodrigues-Neto, José Alvaro

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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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 4 ()
Pages: 207-211

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Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:207-211
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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