The authors extend E. Maskin's results on Nash implementation. First, they establish a condition that is both necessary and sufficient for Nash implementability if there are three or more agents (the case covered by Maskin's sufficiency result). Second--and more important--they examine the two-agent case (for which there existed no general sufficiency results). The two-agent model is the leading case for applications to contracting and bargaining. For this case, too, they establish a condition that is both necessary and sufficient. The authors use their theorems to derive simpler sufficiency conditions that are applicable in a wide variety of economic environments. Copyright 1990 by The Econometric Society.

This paper examines the use of stage mechanisms in implementation problems and provides a partial characterization of the set of subgam e perfect implementable choice rules. It is shown that, in many economic environments, virtually an y choice rule can be implemented. To illustrate the power of this approach, the paper discusses a number of models in which it is possible to implement the first-best (although it wouldn't have been possible to do so without using stage mechanisms). The diversity of these models suggests that subgame perfect implementation may find wide application. Copyright 1988 by The Econometric Society.

We address the monopoly problem of designing and pricing a product line of goods distinguished by different quality and warranty levels. Consumers vary in their evaluations of these attributes, so that the problem is one of screening. It is sufficiently complex that the local approach commonly used does not work. Instead, we use new techniques for dealing with incentive constraints between nonadjacent consumer types. These techniques allow us to characterize optimal allocations that may not be monotonic. In particular, although the more eager types of buyer do pay higher prices and yield the monopoly higher profit, they may receive lower quality or lower warranty coverage. We find preference restrictions that restore monotonicity: concave risk tolerance implies that warranty coverage increases in type, and constant absolute risk aversion implies that quality increases in type.

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It was conjectured by Pigou that an increase in real national income, as reckoned in the prices of either the initial or the terminal period, would always correctly indicate an improvement in national welfare provided the increase referred to the aggregate income of a given group of persons with fixed preferences and a fixed proportional distribution of income among them. We show that if the individual preferences are assumed to be homothetic, and if by a welfare improvement one means respectively a potential improvement (in which losers can be compensated by gainers) or an actual improvement (in which all are gainers), then on either of these respective criteria Pigou's conjecture holds true under these conditions if and only if individual preferences are identical.