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Abstract:
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.

Abstract:
We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A principal determines the number and size of status categories in order to maximize output. We first consider the pure status case without tangible prizes. Our results connect the optimal partition in status categories to properties of the distribution of ability among contestants. The top status category always contains a unique element. For distributions that have an increasing failure rate (IFR), a proliferation of status classes is optimal, whereas the optimal partition involves only two categories if the distribution of abilities is sufficiently concave. Moreover, for IFR distributions, a coarse partition with two status categories achieves at least half of the output obtained in the optimal partition with many categories. Finally, if status is derived solely from monetary rewards, we show that the optimal partition in status classes contains only two categories.

Abstract:
We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A judicious definition of status categories can be used by a principal in order to influence the agents' performance. We first consider a pure status case where there are no tangible prizes. Our main results connect the optimal partition in status categories to various properties of the distribution of ability among contestants. The top status category always contains an unique element. For distributions of abilities that have an increasing failure rate, a proliferation of status classes is optimal, while in other cases the optimal partition involves some coarseness. Finally, we modify the model to allow for status categories that are endogenously determined by monetary prizes of different sizes. If status is solely derived from monetary rewards, we show that the optimal partition in status classes contains only two categories.

Contests, status, normalized spacing, organization design

Abstract:
We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Agents are matched through an intermediary. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), the intermediary's revenue, and the agents' welfare (defined by the total surplus minus payments to the intermediary). In a nutshell, our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than completely random matching, requiring only a minimal amount of information.

Matching, Nonlinear Pricing

Abstract:
We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), an intermediary's revenue, and the agents' welfare (defined by the total surplus minus payments to the intermediary). Following Chao and Wilson (1987) and McAfee (2002), our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than completely random matching, requiring only a minimal amount of information.

Abstract:
Europe has taken the global lead in the issuance of third generation (3G) licences for mobile telecommunications according to the UMTS/IMT-2000 family of standards. We survey the recent European UMTS licence auctions and compare their outcomes with the predictions of a simple auction model that emphasises 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.

Licence auctions, market entry, UMTS

Abstract:
We study optimal contest design in situations where the designer can reward high performance agents with positive prizes and punish low performance agents with negative prizes. We link the optimal prize structure to the curvature of distribution of abilities in the population. In particular, we identify conditions under which, even if punishment is costly, punishing the bottom is more effective than rewarding the top in eliciting effort input. If punishment is costless, we study the optimal number of punishments in the contest.

All-pay auctions, Contests, Order Statistics, Punishments

Abstract:
We study optimal contest design in situations where the designer can reward high performance agents with positive prizes and punish low performance agents with negative prizes. We link the optimal prize structure to the curvature of distribution of abilities in the population. In particular, we identify conditions under which, even if punishment is costly, punishing the bottom is more effective than rewarding the top in eliciting effort input. If punishment is costless, we study the optimal number of punishments in the contest.

Contests, All-pay auctions, Punishments, Order Statistics

Abstract:
We study two-sided markets with a finite numbers of agents on each side, and with two-sided incomplete information. Agents are matched assortatively on the basis of costly signals. A main goal is to identify conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is completely offset by the costs of signalling. We also study how the signalling activity and welfare on each side of the market change when we vary the number of agents and the distribution of their attributes, thereby displaying effects that are particular to small markets. Finally, we look at the continuous version of our two-sided market model and establish the connections to the finite version. Technically, the paper is based on the very elegant theory about stochastic ordering of (normalized) spacings and other linear combinations of order statistics from distributions with monotone failure rates, pioneered by R. Barlow and F. Proschan (1966, 1975) in the framework of reliability theory.

Matching, signalling

Abstract:
We derive conditions on the learning environment - which encompasses both Bayesian and non-Bayesian processes - ensuring that an efficient allocation of resources is achievable in a dynamic allocation environment where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents' values. There are two main kind of conditions: 1) Higher observations should lead to more optimistic beliefs about the distribution of future values; 2) The allowed optimism associated with higher observations needs to be carefully bounded. Our analysis reveals and exploits close, formal relations between the problem of ensuring monotone - and hence implementable - allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem of finding optimal stopping policies for search that are characterized by a reservation price property.

Sequential Assignment, Learning, Dynamic Mechanism Design

Abstract:
We analyze the interplay between license auctions and market structure in a model with several incumbents and several potential entrants. The focus is on the competitiveness induced by the number of auctioned licenses. Under plausible conditions, we show that auctioning more licenses need not result in a more competitive final outcome, contrary to what common sense suggests. This is due to the nature of competition among incumbents, which sometimes exhibits free-riding. We illustrate some results with examples drawn from the recent European license-auctions for third generation (3G) mobile telephony.
We analyze the interplay between license auctions and market structure in a model with several incumbents and several potential entrants. The focus is on the competitiveness induced by the number of auctioned licenses. Under plausible conditions, we show that auctioning more licenses need not result in a more competitive final outcome, contrary to what common sense suggests. This is due to the nature of competition among incumbents, which sometimes exhibits free-riding. We illustrate some results with examples drawn from the recent European license-auctions for third generation (3G) mobile telephony.

Abstract:
We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.

Auction, mixed bundling, revenue maximization

Abstract:
We study two-sided markets with a finite number of agents on each side, and with two-sided incomplete information. Agents are matched assortatively on the basis of costly signals. Asymmetries in signalling activity between the two sides of the market can be explained by asymmetries either in size or in heterogeneity. Our main results identify general conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is offset by the costs of signalling. Finally, we examine the limit model with a continuum of agents and point out differences and similarities to the finite version. Technically, the paper is based on the elegant theory about stochastic order relations among differences of order statistics, pioneered by Barlow and Proschan in 1966 in the framework of reliability theory.

Abstract:
We study the allocation of several heterogenous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson or renewal process. We analyze and compare the policies that maximize either welfare or revenue. We focus on two cases: 1. There is a deadline after which no more objects can be allocated; 2. The horizon is potentially infinite and there is time discounting. We first characterize all implementable allocation schemes, and we compute the expected revenue for any implementable, deterministic and Markovian allocation policy. These properties are shared by the welfare and revenue maximizing policies. Moreover, we show that these policies do not depend on the characteristics of the available objects at each point in time. The revenue-maximizing allocation scheme is obtained by a variational argument which sheds somewhat more light on its properties than the usual dynamic programming approach. We also obtain several properties of the welfare maximizing policy using stochastic dominance measures of increased variability and majorization arguments. These results yield upper/lower bounds on efficiency/revenue for large classes of distributions of agents' characteristics or of distributions of inter-arrival times for which explicit solutions cannot be obtained in closed form.

dynamic pricing, mechanism design, revenue management, sequential assignment

Abstract:
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.

Auctions, externalities, interdependent values

Abstract:
We study contests where several privately informed agents bid for a prize. All bidders bear a cost of bidding that is an increasing function of their bids, and, moreover, bids may be capped. We show that regardless of the number of bidders, if bidders have linear or concave cost functions, then setting a bid cap is not profitable for a designer who wishes to maximize the average bid. On the other hand, if agents have convex cost functions (i.e., an increasing marginal cost), then effectively capping the bids is profitable for a designer facing a sufficiently large number of bidders. Furthermore, bid caps are effective for any number of bidders if the cost functions' degree of the convexity is large enough.

Abstract:
We study an auction whose outcome influences the future interaction among agents. The impact of that interaction on agent i is assumed to be a function of all agents' types (which are private information at the time of the auction). Explicit illustrations treat auctions of patents and takeover contests. We derive equilibria for second-price, sealed-bid auctions in which the seller sometimes keeps the object, and we point out the various effects caused by positive and negative impacts. We also study the effect of reserve prices and entry fees on the seller's revenue and on welfare.

Abstract:
In 1797 Johann Wolfgang von Goethe sold a manuscript through a second-price auction. We investigate Goethe's motivation in the context of the late eighteenth century's book market and relate it to modern auction theory.

Abstract:
We study a model that involves identity-dependent, asymmetric negative external effects. Willingness to pay, which can be computed only in equilibrium, will reflect, besides private valuations, also preemptive incentives stemming from the desire to minimize the negative externalities. We find that the best strategy of some agents is simply not to participate in the market, although they cannot in this way avoid the negative external effects. An illustration is made for the acquisition of patents in oligopolistic markets. Finally, we show that even when we allow full communication and side payments between agents, all coalitional agreements are unstable.