ABSTRACTPartitions of the set of states of nature are the traditional information structures in decision theory. In a multi‐person context, common knowledge of the choices, such as it occurs in a trade, implies common knowledge of relevant information: hence a well‐known impossibility theorem for trade based on differing belief can be obtained. A new set theoretic axiomatization of the beliefs held by decision makers allows here for the construction of doxastic, i.e. possibly incorrect instruments of measurement of the »outside« world, and allow traders to »agree to dis