An important result in convex analysis is the duality between a closed convex set and its support function. We exploit this duality to develop a novel geometric approach to mechanism design. For a general class of social choice problems we characterize the feasible set, which is closed and...

The spectrum for third generation (3G) mobile communications for the German market was alloted to operators by means of an auction. This resulted in a highly competitive outcome: six operators were given rights to provide 3G services. Government revenues from this auction were a staggering EUR...

We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders' underlying valuations We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined...

In a real-time electric power auction, the bids of producers consist of committed supply as a function of price. The bids are submitted under uncertainty, before the demand by the Independent System Operator has been realized. In the Supply Function Equilibrium (SFE), every producer chooses the...

This paper derives a Supply Function Equilibrium (SFE) of a pay-as-bid auction, also called discriminatory auction. Such an auction is used in the balancing market for electric power in Britain. For some probability distributions of demand a pure-strategy equilibrium does not exist. If demand...

Consider a market where producers submit supply functions to a procurement auction - e.g. an electric power auction - under uncertainty, before demand has been realized. In the Supply Function Equilibrium (SFE), every firm commits to the supply function maximizing his expected profit given the...

Within the framework of the common value model, we examine the magnitude of the difference in expected outcome between first-price and second-price sealed bid auctions. The study is limited to two empirical specifications of bidders' signals: Weibull and normal distribution. The optimal bid...

This study empirically examines a sample of national wireless spectrum assignments for the period 2000-2007 to identify the sources of revenue variations. An econometric model that recognises the censored nature of the sample relates per capita winning bid (per Mhz) values to auction design...

The paper characterizes the mixed-strategy equilibria in all-pay auctions with endogenous prizes that depend positively on own effort and negatively on the effort of competitors. Such auctions arise naturally in the context of investment games, lobbying games, and promotion tournaments. We also...