This is a review article of Putting Auction Theory to Work (Cambridge University Press 2004) by Paul Milgrom.

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A, where the subset is interpreted as the set of "welfare optima" A game form (or "mechanism") implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game form (implying, in particular, that a Nash equilibrium exists) and, (ii) all Nash equilibria are welfare optimal. The main result of this paper establishes that any SCR that satisfies two properties—monotonicity and no veto power—can be implemented by a game form if there are three or more individuals. The proof is constructive.

We argue that Arrow’s independence of irrelevant alternatives (IIA) condition is unjustifiably stringent because it rules out making a social welfare function sensitive to individuals’ preference intensities. Accordingly, we propose a modified version of IIA, MIIA, that is a necessary and sufficient relaxation of IIA for taking account of intensities. Rather than obtaining an impossibility result, we show that MIIA together with several other axioms (satisfied by virtually all voting rules and social welfare functions used in practice and studied in theory) uniquely characterizes the Borda count (sometimes called rank-order voting) as a social welfare function.

The soft budget constraint is a syndrome that was identified and studied by Janos Kornai in his analysis of centrally planned economies ( see, Kornai, 1980 ) . The syndrome is said to arise when a seemingly unprofitable enterprise is bailed out by the government or the enterprise’s creditors. In other words, the enterprise is not held to a fixed budget, but finds its budget constraint ‘‘softened’’ by the infusion of additional credit when it is on the verge of failure. Kornai viewed the soft budget constraint as a crucial ingredient for explaining the salient features of socialist economic performance, in particular, the pervasiveness of shortages. One interesting puzzle is why centrally planned economies have been particularly susceptible to the influence of the soft budget constraint; the capitalist world is hardly immune, as the recent financial crisis in Asia attests, but on the whole it has proved less vulnerable. Indeed, the very origin of the soft budget constraint and the mechanism by which it gives rise to shortages and other undesirable effects are also obviously important questions. Although Kornai’s work has long been well known and appreciated, answers to these associated theoretical questions have been hazarded only recently. In Maskin ( 1996 ) , I surveyed some of the initial efforts in this direction, including Mathias Dewatripont and Maskin (1995), which argues that centralization of credit can give rise to soft budget constraints because it facilitates the refinancing of

When economists contemplate the invisible hand at work, they generally think of competitive markets. But there are some circumstances in which markets are not supposed to operate well (i.e., in which the invisible hand is thought to falter). A leading cause of market failure, many argue, is the presence of significant externalities. With such externalities, the first welfare theorem does not apply, and so competitive equilibrium-if it exists at all-is not typically Pareto optimal. In the tradition of A. C. Pigou (1932), the typical response to this lack of optimality is for the government to step in and introduce corrective policy, usually in the form of taxes or subsidies. There is, of course, a strong antiPigouvian tradition, as well. Specifically, proponents of the Coase theorem (Ronald Coase, 1960) have contended that, despite externalities, unrestrained bargaining and contracting ought to be sufficient to generate an efficient outcome. (Indeed Coase's own celebrated example was a case of externalities.) Thus, even if formal markets themselves fail, the invisible hand nevertheless succeeds, and outside intervention or design is not required. Recently, Joseph Farrell (1987) argued that, even when free bargaining is permitted, the laissez-faire conclusion inherent in the Coase theorem may founder if agents have incomplete information about one another's relevant characteristics. I shall show, however, that the problem that Farrell identified is due only to monopoly power and is not peculiar to externalities. Indeed, in this paper, I shall take a modified Coasian stance. I shall attempt to show that, in spite of externalities and incomplete information, private contractual agreements suffice to achieve efficiency, as long as no agent is big enough to have significant market power. This conclusion must be qualified, however, with the proviso that, if the externality is (i.e., no one can be excluded from its effects), the government must intervene to prevent free-riding on the agreements. Intervention, in this case, amounts to establishing the right of an agent providing a positive external effect to collect a fee for increasing the effect from all who enjoy it, even if they are not parties to a contract with the provider. Symmetrically, providers of a negative externality can collect a fee for diminishing the effect from all their victims. In either case, however, the fee is set endogenously, that is, it is determined by the contractual arrangements rather than by the government. This result for nonexcludable externalities (which include pure public goods) provides support for a fairly laissez-faire stance toward externalities but turns on an important assumption, namely, that parties always write contracts so as to maximize their social surplus (subject to incentive and individual-rationality constraints). I will return to this assumption in the final section.

We scrutinize the conceptual framework commonly used in the incomplete contract literature. This literature usually assumes that contractual incompleteness is due to the transaction costs of describing—or of even foreseeing—the possible states of nature in advance. We argue, however, that such transaction costs need not interfere with optimal contracting (i.e. transaction costs need not be relevant), provided that agents can probabilistically forecast their possible future payoffs (even if other aspects of the state of the nature cannot be forecast). In other words, all that is required for optimality is that agents be able to perform dynamic programming, an assumption always invoked by the incomplete contract literature. The foregoing optimality result holds very generally provided that parties can commit themselves not to renegotiate. Moreover, we point out that renegotiation may be hard to reconcile with a framework that otherwise presumes perfect rationality. However, even if renegotiation is allowed, the result still remains valid provided that parties are risk averse.