Characterizing common priors in the form of posteriors

It is shown that if agents cannot agree to disagree then, under an appropriate compactness condition their beliefs are derivable from a common prior-establishing the converse to the agreement theorem of Aumann (1976, Ann. Statist. 4, 1236-1239). This enables us to formulate the existence of a common prior in syntactic terms, i.e., making no use of the space of states of the world, but referring only to the current knowledge and beliefs of the agents. An example demonstrates that the compactness assumption cannot be discarded. Journal of Economic Literature Classification Numbers: C70, D82, D84. (C) 2000 Academic Press.