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. I am grateful to Professor William Thomson for helpful comments and suggestions. I also thank seminar participants in University of Rochester, John Duggan, and François Maniquet. I thank two anonymous referees for their detailed comments, which were very helpful in revising the earlier version. All remaining errors are mine.
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