Simultaneous Ascending Auction

The simultaneous ascending auction has proved to be a successful method of auctioning many related items. Simultaneous sale and ascending bids enable price discovery, which helps bidders build desirable packages of items. Although package bids are not allowed, the auction format does handle mild complementarities well. I examine the auction design and its performance in practice.Auctions, Ascending Auctions, Market Design

How Best to Auction Natural Resources

I study the design of auctions of natural resources, such as oil or mineral rights. A good auction design promotes both an efficient assignment of rights and competitive revenues for the seller. The structure of bidder preferences and the degree of competition are key factors in determining the best design. With weak competition and simple value structures, a simultaneous first-price sealed-bid auction may suffice. With more complex value structures, a dynamic auction with package bids likely is needed to promote efficiency and revenue objectives. Bidding on production shares, rather than bonuses, typically increases government take by reducing oil or mining company risk.Auctions, natural resource auctions, oil auctions

Sequential item pricing for unlimited supply

We investigate the extent to which price updates can increase the revenue of a seller with little prior information on demand. We study prior-free revenue maximization for a seller with unlimited supply of n item types facing m myopic buyers present for k < log n days. For the static (k = 1) case, Balcan et al. [2] show that one random item price (the same on each item) yields revenue within a \Theta(log m + log n) factor of optimum and this factor is tight. We define the hereditary maximizers property of buyer valuations (satisfied by any multi-unit or gross substitutes valuation) that is sufficient for a significant improvement of the approximation factor in the dynamic (k > 1) setting. Our main result is a non-increasing, randomized, schedule of k equal item prices with expected revenue within a O((log m + log n) / k) factor of optimum for private valuations with hereditary maximizers. This factor is almost tight: we show that any pricing scheme over k days has a revenue approximation factor of at least (log m + log n) / (3k). We obtain analogous matching lower and upper bounds of \Theta((log n) / k) if all valuations have the same maximum. We expect our upper bound technique to be of broader interest; for example, it can significantly improve the result of Akhlaghpour et al. [1]. We also initiate the study of revenue maximization given allocative externalities (i.e. influences) between buyers with combinatorial valuations. We provide a rather general model of positive influence of others' ownership of items on a buyer's valuation. For affine, submodular externalities and valuations with hereditary maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing strategy based on our algorithm for private valuations. This strategy preserves our approximation factor, despite an affine increase (due to externalities) in the optimum revenue.Comment: 18 pages, 1 figur

Composable and Efficient Mechanisms

We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple different mechanisms simultaneously or sequentially. We define the class of smooth mechanisms, related to smooth games defined by Roughgarden, that can be thought of as mechanisms that generate approximately market clearing prices. We show that smooth mechanisms result in high quality outcome in equilibrium both in the full information setting and in the Bayesian setting with uncertainty about participants, as well as in learning outcomes. Our main result is to show that such mechanisms compose well: smoothness locally at each mechanism implies efficiency globally. For mechanisms where good performance requires that bidders do not bid above their value, we identify the notion of a weakly smooth mechanism. Weakly smooth mechanisms, such as the Vickrey auction, are approximately efficient under the no-overbidding assumption. Similar to smooth mechanisms, weakly smooth mechanisms behave well in composition, and have high quality outcome in equilibrium (assuming no overbidding) both in the full information setting and in the Bayesian setting, as well as in learning outcomes. In most of the paper we assume participants have quasi-linear valuations. We also extend some of our results to settings where participants have budget constraints

Efficiency Resource Allocation for Device-to-Device Underlay Communication Systems: A Reverse Iterative Combinatorial Auction Based Approach

Peer-to-peer communication has been recently considered as a popular issue for local area services. An innovative resource allocation scheme is proposed to improve the performance of mobile peer-to-peer, i.e., device-to-device (D2D), communications as an underlay in the downlink (DL) cellular networks. To optimize the system sum rate over the resource sharing of both D2D and cellular modes, we introduce a reverse iterative combinatorial auction as the allocation mechanism. In the auction, all the spectrum resources are considered as a set of resource units, which as bidders compete to obtain business while the packages of the D2D pairs are auctioned off as goods in each auction round. We first formulate the valuation of each resource unit, as a basis of the proposed auction. And then a detailed non-monotonic descending price auction algorithm is explained depending on the utility function that accounts for the channel gain from D2D and the costs for the system. Further, we prove that the proposed auction-based scheme is cheat-proof, and converges in a finite number of iteration rounds. We explain non-monotonicity in the price update process and show lower complexity compared to a traditional combinatorial allocation. The simulation results demonstrate that the algorithm efficiently leads to a good performance on the system sum rate.Comment: 26 pages, 6 fgures; IEEE Journals on Selected Areas in Communications, 201

How Best to Auction Oil Rights

I study the design of oil rights auctions. A good auction design promotes both an efficient assignment of rights and competitive revenues for the seller. The structure of bidder preferences and the degree of competition are key factors in determining the best design. With weak competition and additive values, a simultaneous first-price sealed-bid auction may suffice. With more complex value structures, a dynamic auction with package bids, such as the clock-proxy auction, likely is needed to promote the efficiency and revenue objectives. Bidding on production shares, rather than bonuses, typically increases government take by reducing oil company risk.Auctions, Oil Auctions, Market Design, Clock Auctions

Competition Between Auctions

Even though auctions are capturing an increasing share of commerce, they are typically treated in the theoretical economics literature as isolated. That is, an auction is typically treated as a single seller facing multiple buyers or as a single buyer facing multiple sellers. In this paper, we review the state of the art of competition between auctions. We consider three different types of competition: competition between auctions, competition between formats, and competition between auctioneers vying for auction traffic. We highlight the newest experimental, statistical and analytical methods in the analysis of competition between auctions.auctions, bidding, competition, auction formats, auction houses

On the Inefficiency of the Uniform Price Auction

We present our results on Uniform Price Auctions, one of the standard sealed-bid multi-unit auction formats, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and economically efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general. The uniform pricing rule is, however, widely popular by its appeal to the natural anticipation, that identical items should be identically priced. In this work we study equilibria of the Uniform Price Auction for bidders with (symmetric) submodular valuation functions, over the number of units that they win. We investigate pure Nash equilibria of the auction in undominated strategies; we produce a characterization of these equilibria that allows us to prove that a fraction 1-1/e of the optimum social welfare is always recovered in undominated pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we study the auction under the incomplete information setting and prove a bound of 4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor corrections on the previous version

Optimal Auctions vs. Anonymous Pricing

For selling a single item to agents with independent but non-identically distributed values, the revenue optimal auction is complex. With respect to it, Hartline and Roughgarden (2009) showed that the approximation factor of the second-price auction with an anonymous reserve is between two and four. We consider the more demanding problem of approximating the revenue of the ex ante relaxation of the auction problem by posting an anonymous price (while supplies last) and prove that their worst-case ratio is e. As a corollary, the upper-bound of anonymous pricing or anonymous reserves versus the optimal auction improves from four to $e$. We conclude that, up to an $e$ factor, discrimination and simultaneity are unimportant for driving revenue in single-item auctions.Comment: 19 pages, 6 figures, To appear in 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2015