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.

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.

We first point out that the recent property-rights literature is based on three assumptions: (1) that contracts are always subject to renegotiation; (2) that the exercise of a property right confers a private benefit and (3) that parties are risk-neutral. Building on Hart-Moore (1999), we provide conditions under which an optimal contract consists of nothing more than an assignment of property rights. We also examine the robustness of some of the literature's standard predictions about asset ownership to the introduction of mechanisms for eliciting parties' ex post willingness to pay for the assets (such as options or financial markets). To illustrate the issue, we revisit the Hart-Moore (1990) proposition that joint ownership is suboptimal, and argue that ownership by a single party is dominated by joint ownership with put options.