We identify general domain properties that induce the non-existence of efficient, strategy-proof, and non-dictatorial rules in the 2-agent exchange economy. Applying these properties, we establish the impossibility result in several restricted domains; the "intertemporal exchange problem" (without saving technology) with preferences represented by the discounted sum of a temporal utility function, the "risk sharing problem" with risk averse expected utility preferences, the CES-preference domain, etc. None of the earlier studies applies to these domains.

Keywords: Strategy-proofness, efficiency, restricted domain, dictatorship.