From posteriors to priors via cycles: An addendum - Martin Hellwig (Max Planck Institute for Research on Collective Goods, 2011)
Rodrigues-Neto (2009) has shown that a given specification of posteriors of different players in an incomplete-information setting is compatible with a common prior if and only if the posteriors satisfy the so-called cycle equations. This note shows that, if, for any player, any element of the partition of the this player has a nonempty intersection with any element of the partition of any other player, then it suffices to verify the cycle equations for all cycles of length 4 or less.
Keywords: D82; D83; 330; belief systems; consistency; common priors; cycle equations; Spieltheorie; Unvollkommene Information; Wissen; Theorie