Cycles of length two in monotonic models

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 …nite 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 [9]. Key words: acyclic, cycle, knowledge, monotonicity, order, partition, posterior, prior. JEL Classi…cation: C02, D80, D82, D83. Research School of Economics, Australian National University, Canberra ACT 0200, Australia. I would like to thank Scott McCracken and James Taylor for comments, and Merrilyn Lárusson for the English editing. All remaining errors are my own responsibility. URL: www.jarodriguesneto.com. E-mail: [email protected].