Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Priority Auctions and Queue Disciplines that Depend on Processing Time

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before, or after service). In both schemes, a customer obtains priority over all customers (waiting in the queue or arriving while he is waiting) who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue-discipline (i.e., SPT, LPT) arising in a bidding equilibrium

A note of revenue maximization and efficiency in multi-object auctions

Combining the result of Palfrey (1983) about the role of bundling and the revenue equivalence theorem, this note shows that there is a conflict between revenue maximization and efficiency in multi-object auctions even with symmetric bidders.efficiency

Priority Auctions and Queue Disciplines that Depend on Processing Time

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before, or after service). In both schemes, a customer obtains priority over all customers (waiting in the queue or arriving while he is waiting) who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue-discipline (i.e., SPT, LPT) arising in a bidding equilibrium.

The European UMTS/IMT-2000 License Auctions

We survey the recent European UMTS license auctions and compare their outcomes with the predictions of a simple model that emphasizes future market structure as a main determinant of valuations for licenses. Since the main goal of most spectrum allocation procedures is economic efficiency, and since consumers (who are affected by the ensuing market structure) do not participate at the auction stage, good designs must alleviate the asymmetry among incumbents and potential entrants by actively encouraging entry.

Efficient Design with Interdependent Valuations

We study efficient, Bayes-Nash incentive compatible mechanisms in a social choice setting that allows for informational and allocative externalities. We show that such mechanisms exist only if a congruence condition relating private and social rates of information substitution is satisfied. If signals are multidimensional, the congruence condition is determined by an integrability constraint, and it can hold only in non-generic cases such as the private value case or the symmetric case. If signals are one-dimensional, the congruence condition reduces to a monotonicity constraint and it can be generically satisfied. We apply the results to the study of multi-object auctions, and we discuss why such auctions cannot be reduced to one-dimensional models without loss of generality.

A Note on Revenue Maximization and Efficiency in Multi-Object Auctions

We consider an auction with risk neutral agents having independent private valuations for several heterogenous objects. Most of the literature on revenue-maximizing auctions has focused on the sale of one good or on the sale of several identical units (thus yielding one-dimensional informational models). Two reasons for inefficiency in revenue-maximizing auctions have been identified 1) The (monopolist) seller can increase revenue by restricting supply. 2) A revenue maximizing seller will sell to bidders with the highest ''virtual'' valuations (see Myerson, 1981). Virtual valuations are adjusted valuations that take into account bidders' informational rents, and depend on the distribution of private information. Asymmetries among bidders (and possibly other properties of these distributions) drive a wedge between virtual and true valuations, leading to inefficiencies (see Ausubel and Cramton, 1998 for a recent discussion of these issues). Our purpose here is to illustrate in the simplest possible way that a revenue-maximizing seller of several heterogenous objects has incentives to ''misallocate'' the sold objects even in symmetric settings, and no matter what the (symmetric) function governing the distribution of private information is. This inefficiency result should be contrasted with the efficiency result in Armstrong (1998) that applies only to some cases with discrete distributions of valuations.

The German UMTS Design: Insights From Multi-Object Auction Theory

We briefly survey several insights about value and revenue maximization in multi-object auctions and apply them to the German (and Austrian) UMTS auction. In particular, we discuss in detail the exposure problem that caused firms in Germany to pay almost Euro 20 billion for nothing.