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 impossibility results in several restricted domains; for example, 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 examples.
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