Explore the vast range of titles available.

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.

We analyze optimal mechanisms in environments where sellers are privately informed about quality. A methodology is provided for deriving conditions that are necessary and sufficient to determine when two simple trading environments maximize either social or private surplus. The commonly used auction mechanism is frequently inefficient in procurement environments. Often, the optimal mechanism is simply to order potential suppliers and to tender take-it-or-leave-it offers to each sequentially. We completely characterize the environments in which either mechanism is optimal. In doing so, we develop a general methodology that determines when and if a given trading institution is optimal.

Well-behaved infinite signaling games may have no sequential equilibria. We prove that adding cheap talk to these games \"solves\" the nonexistence problem: the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap-talk extension of the limit game. In addition, when the signaling space has no isolated points, any cheap-talk sequential equilibrium outcome can be approximated by a sequential ε-equilibrium of the game without cheap talk.

For a class of infinite signaling games, the perfect Bayesian equilibrium strategies of finite approximating games converge to equilibrium strategies of the infinite game. This proves the existence of perfect Bayesian equilibrium for that class of games. It is well known that in general, equilibria may not exist in infinite signaling games.

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 sequences of economies with uniformly bounded core allocations may fail to exhibit equivalence properties. Sufficient conditions to restore convergence are provided.

Changes in the parameters of an n-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight the existence of a common thread, our \"own effect\" assumption, in formally diverse areas of economics. We discuss several applications; among them we establish the existence of efficient equilibria in English auctions with interdependent valuations, and a version of the Stopler-Samuelson Theorem for an n X n trade model.

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.

Signaling games with infinite action spaces may have no sequential equilibrium. We prove that adding cheap talk to these games solves the non-existence problem; the sequential equilibrium outcome correspondence is upper hemi-continuous. In addition, when the signaling space has sufficiently many signals, any cheap talk sequential equilibrium outcome can be appproximated by a sequential (e)-equilibrium of the game without cheap talk. In these cases, adding cheap talk does not fundamentally alter the nature of the game.

An example shows that there are well-behaved infinte signaling games with no sequential equilibria. We explore the relationship between equilibrium outcomes of the infinite game and those of approximating games. Consider a sequence of signaling games approaching a limit game. A \"(sub)sequence of equilibrium outcomes of the approximating games will converge to a limit distribution. That limit distribution will be an equilibrium outcome of the limit game if it can be realized by strategies of the limit game. As a result of this general convergence result, we prove the existance of sequential and weak-best-response equilibria for strongly monotonic games. In a companion article we explore the role of cheap talk in solving the non-existence problem.

We examine market-clearing prices and allocations in economies where agents' demand functions are undominated relative to their beliefs about other agents' actions. For sufficiently large economies and give certain restrictions on beliefs, the resulting allocations are nearly competitive.