International Journal of Game Theory

, Volume 43, Issue 2, pp 403–413

Monotonic models and cycles


DOI: 10.1007/s00182-013-0385-7

Cite this article as:
Rodrigues-Neto, J.A. Int J Game Theory (2014) 43: 403. doi:10.1007/s00182-013-0385-7


A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posteriors for the players is consistent (i.e., there is a common prior). When checking for consistency in a monotonic model, it is not necessary to evaluate all cycle equations; if the cycle equations corresponding to cycles of length two hold, then there is a common prior.


Acyclicity Cycle Knowledge Monotonicity Partition Posterior Prior 

JEL Classification

C02 D80 D82 D83. 

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Research School of EconomicsAustralian National UniversityCanberraAustralia

Personalised recommendations