No trade and yes trade theorems for heterogeneous priors

We show that contrary to currently widely-held misperceptions, the classical no trade theorem obtains even under heterogeneous priors. That is, when priors are not common, speculative trade is still impossible under common knowledge of rationality. However, trade becomes mutually acceptable if at least one party to the trade puts at least some slight probability on the other party being irrational. We also derive bounds on disagreements in the case of heterogeneous priors and common p-beliefs.