Putting auction theory to work : the simultaneous ascending auction

The"simultaneous ascending auction"was first introduced in 1994 to sell licenses to use bands of radio spectrum in the United States. Much of the attention devoted to the auction came from its role in reducing federal regulation of the radio spectrum and allowing market values, rather than administrative fiat, to determine who would use the spectrum resource. Several parts of economic theory proved helpful in designing the rules for simultaneous ascending auction and in thinking about how the design might be improved and adapted for new applications. After briefly reviewing the major rules of the auction in section 2, the author turns in section 3 to an analysis based on tatonnement theory, which regards the auction as a mechanism for discovering an efficient allocation and its supporting prices. The analysis reveals a fundamental difference between situations in which the licenses are mutual substitutes and others in which the same licenses are sometimes substitutes and sometimes complements. Section 4 is a selective account of some applications of game theory to evaluating the simultaneous ascending auction design for spectrum sales. Results like those reported in section 3 have led to renewed interest in auctions in which bids for license packages are permitted. In section 5, the author uses game theory to analyze the biases in a leading proposal for dynamic combinatorial bidding. Section 6 briefly answers two additional questions that economists often ask about auction design: If trading of licenses after the auction is allowed, why does the auction form matter at all for promoting efficient license assignments? Holding fixed the quantity of licenses to be sold, how sharp is the conflict between the objectives of assigning licenses efficiently and obtaining maximum revenue? Section 7 concludes.Economic Theory&Research,International Terrorism&Counterterrorism,Markets and Market Access,Environmental Economics&Policies,Labor Policies,Markets and Market Access,Access to Markets,Economic Theory&Research,Environmental Economics&Policies,International Terrorism&Counterterrorism

Suspension and levitation in nonlinear theories

I investigate stable equilibria of bodies in potential fields satisfying a generalized Poisson equation: divergence[m(grad phi) grad phi]= source density. This describes diverse systems such as nonlinear dielectrics, certain flow problems, magnets, and superconductors in nonlinear magnetic media; equilibria of forced soap films; and equilibria in certain nonlinear field theories such as Born-Infeld electromagnetism. Earnshaw's theorem, totally barring stable equilibria in the linear case, breaks down. While it is still impossible to suspend a test, point charge or dipole, one can suspend point bodies of finite charge, or extended test-charge bodies. I examine circumstances under which this can be done, using limits and special cases. I also consider the analogue of magnetic trapping of neutral (dipolar) particles.Comment: Five pages, Revtex, to appear in Physics Letters

Complementarities and systems: Understanding japanese economic organization

The performance of the Japanese economy in the last forty five years, during which it has gone from post war destitution and near collapse to one of the richest and most productive in the world is unmatched in human history. The purposes of this essay are to interpret both the characteristic features of Japanese economic organization in terms of the concept of complementarity, and some recent developments in Japanese economy, and to speculate on its future.

Concepts and Properties of Substitute Goods

We distinguish two notions of substitutes for discrete inputs of a firm. Class substitutes are defined assuming that units of a given input have the same price while unitary substitutes treat each unit as a distinct input with its own price. Unitary substitutes is necessary and sufficient for such results as the robust existence of equilibrium, the robust inclusion of the Vickrey outcome in the core, and the law of aggregate demand, while the class substitutes condition is necessary and sufficient for robust monotonicity of certain auction/tatonnement processes. We analyze the concept of pseudo-equilibrium which extends, and in some sense approximates, the concept of equilibrium when no equilibrium exists. We characterize unitary substitutes as class substitutes plus two other properties. We extend the analysis to divisible inputs, with a particular focus on robustness of the concepts and their relation to the generalized law of aggregate demand.