Agreeing to Agree and Trade

Abstract

We study when agents can have posteriors with a common prior such that it is common knowledge that the posteriors for an event E coincide. For any finite number of agents, we recast this possibility of agreeing to agree as the existence of a common prior which solves a linear system of homogeneous equations. The formulation yields a dual characterization of agreeing to agree in terms of state-contingent trades: agreeing to agree is possible if and only if no trade based on the ocurrance of E generates a risk-free arbitrage opportunity. We use our results to characterize agreeing to agree with more than two agents in terms of information structure. In particular, the condition of common knowledge of ignorance proposed by Lehrer and Samet (2011) is no longer sufficient.