Alejandro M. Manelli

Optimal Procurement Mechanisms

The procurement of supplies is often conducted through the buyer analogue of an auction. Sealed bids are submitted and the contract is awarded to the lowest bidder. Although this method may be an optimal way of selling an object, an additional complication arises in the case of purchasing a good. When sellers are privately informed about the quality of the good to be sold, these mechanisms typically result in the provision of the lowest quality object. This paper characterizes optimal mechanisms in environments where sellers are privately informed about quality. It shows that the commonly used auction mechanism is privately or socially optimal in only a small class of environments. In another plausible set of environments the optimal mechanism is simply to order potential supplies and to tender take-it-or-leave-it offers to each sequentially. We use the duality theorem of linear programming to provide a methodology by which necessary and sufficient conditions can be derived to determine when any incentive compatible trading environment maximizes social or private surplus.

Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly

The seller of N distinct objects is uncertain about the buyer’s valuation for those objects. The seller’s problem, to maximize expected revenue, consists of maximizing a linear functional over a convex set of mechanisms. A solution to the seller’s problem can always be found in an extreme point of the feasible set. We identify the relevant extreme points and faces of the feasible set. With N = 1, the extreme points are easily described providing simple proofs of well-known results. The revenue-maximizing mechanism assigns the object with probability one or zero depending on the buyer’s report. With N > 1, extreme points often involve randomization in the assignment of goods. Virtually any extreme point of the feasible set maximizes revenue for a well-behaved distribution of buyer’s valuations. We provide a simple algebraic procedure to determine whether a mechanism is an extreme point.

Bundling as an optimal selling mechanism for a multiple-good monopolist

Abstract Multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price–bundle pair of his choice. We identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules. We then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n -object case. We use these results to characterize environments, mainly distributions of valuations, where bundling is the optimal mechanism in the two and three good cases.

Bayesian and Dominant-Strategy Implementation in the Independent Private-Values Model

We prove—in the standard independent private-values model—that the outcome, in terms of interim expected probabilities of trade and interim expected transfers, of any Bayesian mechanism can also be obtained with a dominant-strategy mechanism.

Monotonic Preferences and Core Equivalence

Examples of well-behaved sequences of economies, without monotonic preferences, are constructed. These economies have core allocations that cannot be decentralized by prices, even in a weak sense. Relaxing the monotonicity assumption results in core allocations that are not uniformly integrable, breaking the connection between the continuum and the large finite model. If, in addition, preferences are nonconvex, even uniformly bounded core allocations may fail to converge in a well sense. Sufficient conditions to restore convergence are provided. Copyright 1991 by The Econometric Society.

Subgame Perfect Equilibria in Stage Games

Abstract It is well known that a stage game with infinite choice-sets, unless it contains a public coordination-device in each stage, may have no subgame perfect equilibria. We show that if a game with public coordination-devices has a subgame perfect equilibrium in which two players in each stage use non-atomic strategies, then the game without coordination devices also has a subgame perfect equilibrium. Journal of Economic Literature Classification Numbers: C6, C7, D8.