The cycles approach

José Rodrigues-Neto

Journal of Mathematical Economics, 2012, vol. 48, issue 4, 207-211

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.

Keywords: Consistency; Cycle; Cyclomatic; Prior; Posterior (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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Working Paper: The Cycles Approach (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:48:y:2012:i:4:p:207-211

DOI: 10.1016/j.jmateco.2012.05.002

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