Self-consistency, consistency and cycles in non-partitional knowledge models

This paper expands the correspondence model of knowledge to a framework where there is an objective and many subjective state spaces, one for each player. At every objective state, each player lists the subset of her subjective states that she considers possible. In this context, the question of “self-consistency” arises: given beliefs of a player, is it possible that all of these beliefs come from a common prior via Bayesian updating? This paper provides necessary and sufficient conditions for self-consistency. If all players are self-consistent, the question of consistency arises: is there a common prior that rationalizes the beliefs of all players? Is it possible that self-consistency or consistency holds regardless of the numerical values of beliefs of the players? This paper provides necessary and sufficient conditions for consistency of beliefs.