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 prepackaged 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. 1

Ascending auctions with package bidding and their economic uses are explained and the main results of recent FCC-sponsored experiments with such auctions are summarized. A benchmark model is formulated that accounts for the experimental results. In the benchmark, if each bidder bids "straightforwardly" at each round for its potentially most profitable package, then the total payoff is approximately maximized by the final allocation---all payoff approximations here have error bounds proportional to the bid increment. With just two bidders, straightforward bidding strategies constitute an approximate equilibrium, but there can also be other equilibria. A bidder whose competitors all bid straightforwardly has a best reply that entails bidding straightforwardly but with maximal delays, suggesting a concern for the auctions time-to-completion. A new class of simple "bid improvement rules" is introduced that prevents such delays and accelerates the auction without unnecessarily degrading auction performance relative to the unmodified benchmark. The results are used to formulate recommendations for the FCC auction design. 1.

Search engines commonly use “sponsored links”, where certain advertisers ’ links are pro-moted to be placed above others in return for monetary payment. It is natural to assume that all providers value a higher ranked placement more than lower ranked ones. Then how should the seller optimally sell these ranked slots is critical for the search engines. In this paper we study the seller’s (search engine) optimal selling mechanism in the following setting: buyers (advertisers), each of whom has unit demand, compete for positions offered by the seller. While each buyer’s valuation for each position is private and independent, the ranking for these positions is common among all the buyers. However the rate at which these valuations change might be different. We begin with 4 simplified scenarios specifying how buyers valuations change for different positions, namely,“parallel”, “convergent”, “di-vergent”, and “convergent then divergent”. We find that the optimal incentive compatible allocation mechanism is quite different in determining the “pivot ” types and the order to fill in the positions. Under some conditions, these mechanisms are even efficient in terms of maximizing the total welfare of the auctioneer and bidders. When the buyers ’ valuations for lower positions decrease at different rates, the seller earns more than the case of simple second-price sequential auction.

This paper proposes a novel policy to motivate private-sector operators of basic infrastructure to expand infrastructure into previously unserved regions. It is particularly useful when resources are transferred to the private sector, as occurs during the privatization of a state-owned telecommunications carrier, the introduction of competition, the release of spectrum, or the allocation of cash subsidies for this purpose. Firms receive tradable universal service obligations in the form of milestones that must be met, and commitments to meet specific deadlines. By exchanging its commitments, a firm can increase or decrease the rate at which it must expand infrastructure. By exchanging milestones, a firm can change where it must expand infrastructure. Making milestones and commitments independent and fully tradable allows each firm to develop the most cost effective business strategy possible, and to adapt that strategy as technology and demand evolve over time. The exchange of mileston...

We study auctions for a set of ranked items where each buyer has a unit demand. This setting has promising applications in areas such as keyword auctions in the search engine advertising industry, the sale of quality ranked raw materials, etc. An auction mechanism suitable for this setting is the simultaneous pooled auction (SPA), where each bidder simultaneously submits a single bid and is allocated an object based on the rank of his bid among all the bids. We study how to improve the seller’s expected revenue by enforcing a reserve price in a SPA. We find that the use of the reserve price significantly increases the seller’s revenue, especially when the number of items for sale is relatively large compared to the number of participating bidders. One severe problem inherent in the SPA is that some bidders may incur ex post losses; that is, they pay more than what they value the received objects. We propose a tailored VCG mechanism that generates the same expected revenue as the SPA does, while bidders do not incur any ex post loss. We also discuss the potential applications of this research

We analyze competitive pressures in a sequence of auctions with a growing number of bidders, in a model that includes private and common valuations as special cases. We show that the key determinant of bidders' surplus (and implicitly auction revenue) is how the goods are distributed. In any setting and sequence of auctions where the allocation of good(s) is concentrated among a shrinking proportion of the population, the winning bidders enjoy no surplus in the limit. If instead the good(s) are allocated in a dispersed manner so that a non-vanishing proportion of the bidders obtain objects, then in any of a wide class of auctions bidders enjoy a surplus that is bounded away from zero. Moreover, under dispersed allocations, the format of the auction matters. If bidders have constant marginal utilities for objects up to some limit, then uniform price auctions lead to higher revenue than discriminatory auctions. If agents have decreasing marginal utilities for objects, then uniform price auctions are asymptotically efficient, while discriminatory auctions are asymptotically inefficient. Finally, we show that in some cases where dispersed allocations are efficient, revenue may increase by bundling goods at the expense of efficiency.

Developing countries often strive to extend basic telecommunications services to rural and remote areas. Wealthier nations sometimes face similar challenges with other services. This paper proposes a novel policy to motivate private-sector operators of basic infrastructure to expand infrastructure into previously unserved regions. It is particularly useful when resources are transferred to the private sector, as occurs during the privatization of a state-owned telecommunications carrier, the introduction of competition, the release of spectrum, or the allocation of cash subsidies for this purpose. Firms receive tradable universal service obligations in the form of milestones that must be met, and commitments to meet specific deadlines. By exchanging its commitments, a firm can increase or decrease the rate at which

This paper uses data detailing ransom prices and time to ransom for over 10,000 captives rescued from the Barbary Corsairs between 1575 and 1739 to investigate the empirical relevance of dynamic bargaining models with one-sided asymmetric information. Our unique dataset includes information that only the buyer knew. In addition, we observe multiple negotiations that were similar (ex ante) from the uninformed party’s (seller’s) point of view. Empirical results suggest that existing dynamic bargaining models have substantial explanatory power both regarding the evolution of prices over time as well as how a variety of other factors affected bargaining outcomes. In particular, variation in the costs of bargaining between two corsair strongholds helps explain many of the observed outcome differences. ∗Harvard University and NBER. Harvard University. We thank seminar participants at Stanford and NYU Abu Dhabi for helpful comments and discussions. The library staff at the Biblioteca Nacional de Madrid and the Archivo Histórico Nacional facilitated the data collection. Judith Gallego provided outstanding research assistance. Any remaining errors are our own. 1 1

Mechanisms are present everywhere in both business and social contexts. They govern the interactions people have with businesses, governments, and each other. One emerging trend over the past decade is a demand for higher levels of expressiveness in mechanisms that mediate interactions such as the allocation of resources, matching of peers, and elicitation of opinions. This trend has already manifested itself in combinatorial auctions and generalizations thereof. It is also reflected in the richness of preference expression offered by businesses as diverse as matchmaking sites, sites like Amazon and Netflix, and services like Google’s AdSense. In Web 2.0 parlance, this demand for increasingly diverse offerings is called the Long Tail. A driving force behind this trend is that greater expressiveness begets better matches, or greater efficiency of the outcomes. Yet, expressiveness does not come for free; it burdens users to specify more preference information. Today’s mechanisms have relied on empirical tweaking to determine how to deal with this and related tradeoffs. In this thesis, we propose to establish the foundations of expressiveness in mechanisms and its relationship to their efficiency,

This paper designs the optimal mechanism for selling a set of commonly-ranked objects. While buyers rank these objects in the same order, the rates at which their valuations change for a less-preferred object might be different. Four stylized cases are identified according to this difference: “parallel,” “convergent,” “divergent,” and “convergent then divergent. ” The optimal mechanism imposes a reserve price for each of the positions. Depending on which of the four stylized cases is considered, a higher-type bidder may be allocated a higher-ranked or lower-ranked position. There is also a positive probability that a higher-ranked object is not allocated while a lower-ranked one is allocated. In a departure from the extant mechanism-design literature, the individual-rationality (IR) constraint for a mid-range type of bidder can be binding.