From Posteriors to Priors via Cycles: An Addendum

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.Belief systems, consistency, common priors, cycle equations

Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors

The paper provides a speci?cation of belief systems for models of large economies with anonymity in which aggregate states depend only on cross-section distributions of types. For belief systems satisfying certain conditions of mutual absolute continuity, the paper gives a necessary and sufficient condition for the existence of a common prior. Under the given conditions, the common prior is unique.Large Economy, Belief systems, consistency, common prior

From posteriors to priors via cycles

We present new necessary and sufficient conditions for checking if a set of players' posteriors may come from a common prior. A simple diagrammatic device calculates the join and meet of players' knowledge partitions. Each cycle in the diagram has a corresponding cycle equation. Posteriors are consistent with a common prior if and only if all cycle equations are satisfied. We prove that in games of two players, where the join partition has only singletons, a common prior exists if each player's distribution of beliefs over the elements of her opponent's partition is independent of her own private information. Crow

From posteriors to priors via cycles

We present new necessary and sufficient conditions for checking if a set of players' posteriors may come from a common prior. A simple diagrammatic device calculates the join and meet of players' knowledge partitions. Each cycle in the diagram has a corresponding cycle equation. Posteriors are consistent with a common prior if and only if all cycle equations are satisfied. We prove that in games of two players, where the join partition has only singletons, a common prior exists if each player's distribution of beliefs over the elements of her opponent's partition is independent of her own private information.Consistency Cycle Incomplete information Join Knowledge Meet Partition Prior Posterior Type

From Posteriors to Priors via Cycles: An Addendum

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