Core-competitive Auctions

One of the major drawbacks of the celebrated VCG auction is its low (or zero) revenue even when the agents have high value for the goods and a {\em competitive} outcome could have generated a significant revenue. A competitive outcome is one for which it is impossible for the seller and a subset of buyers to `block' the auction by defecting and negotiating an outcome with higher payoffs for themselves. This corresponds to the well-known concept of {\em core} in cooperative game theory. In particular, VCG revenue is known to be not competitive when the goods being sold have complementarities. A bottleneck here is an impossibility result showing that there is no auction that simultaneously achieves competitive prices (a core outcome) and incentive-compatibility. In this paper we try to overcome the above impossibility result by asking the following natural question: is it possible to design an incentive-compatible auction whose revenue is comparable (even if less) to a competitive outcome? Towards this, we define a notion of {\em core-competitive} auctions. We say that an incentive-compatible auction is $\alpha$-core-competitive if its revenue is at least $1/\alpha$ fraction of the minimum revenue of a core-outcome. We study the Text-and-Image setting. In this setting, there is an ad slot which can be filled with either a single image ad or $k$ text ads. We design an $O(\ln \ln k)$ core-competitive randomized auction and an $O(\sqrt{\ln(k)})$ competitive deterministic auction for the Text-and-Image setting. We also show that both factors are tight

Optimal Competitive Auctions

We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity

Ascending auctions: some impossibility results and their resolutions with final price discounts

When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.ascending auctions ; combinatorial auctions ; bidder-optimal competitive equilibrium ; non-linear pricing ; Vickrey payoffs ; increments

Auctioning Rough Diamonds: A Competitive Sales Process for BHP Billiton’s Ekati Diamonds

We describe a new approach for selling rough diamonds through competitive auctions. The classical approach of De Beers—giving each customer a bag of stones and a take-it-or-leave-it price—worked well in near monopoly circumstances, but is ill-suited for competitive producers. Competitive producers, like BHP Billiton, benefit from getting the diamonds to those who value them the most. Beginning in 2008, BHP Billiton introduced a simple auction process to assign its Ekati diamonds to the highest bidders at competitive market prices. A Spot auction, ten times per year, is used to establish prices for each of nineteen deals of diamonds grouped by size, color, and quality. A Term auction allows customers to lock in a long-term supply commitment at prices indexed to future Spot auctions. A Specials auction, two or three times per year, prices large stones. The auctions use an ascending-clock format in which prices increase for each product until there is no excess demand. This approach allows customers to discover market prices, while managing portfolio and budget constraints. The approach has proven remarkably successful in pricing and allocating the mine’s output even in the face of the global financial crisis.diamond auctions, market design

Competitive Auctions: Theory and Application

The theory of competitive auctions offers a coherent framework for modelling coordination frictions as a non-cooperative game. The theory represents an advancement over cooperative approaches that make exogenous assumptions about how output is divided between buyers and sellers and about the forces that bring buyers and sellers into local markets. Moreover, unlike price posting models, which fix the terms of trade prior to matching, competitive auction models have a bidding process that allocates the good (or service) to the highest valuation bidder at a price equal to the second highest valuation. Therefore, the competing auction model is more robust to problems in which there are heterogenous valuations. This paper develops the theory of competitive auctions and applies it to a number of practical problems in microeconomics, labor economics, industrial organization, investment theory and monetary economics.

Competitive Auctions: Theory and Application

The theory of competitive auctions offers a coherent framework for modelling coordination frictions as a non-cooperative game. The theory represents an advancement over cooperative approaches that make exogenous assumptions about how output is divided between buyers and sellers and about the forces that bring buyers and sellers into local markets. Moreover, unlike price posting models, which fix the terms of trade prior to matching, competitive auction models have a bidding process that allocates the good (or service) to the highest valuation bidder at a price equal to the second highest valuation. Therefore, the competitive auction model is more robust to problems in which there are heterogenous valuations. This paper develops the theory of competitive auctions and applies it to a number of practical problems in microeconomics, labor economics, industrial organization, investment theory and monetary economics.

Bidding for Complex Projects: Evidence From the Acquisitions of IT Services

Competitive bidding (as auctions) is commonly used to procure goods and services. Public buyers are often mandated by law to adopt competitive procedures to ensure transparency and promote full competition. Recent theoretical literature, however, suggests that open competition can perform poorly in allocating complex projects. In exploring the determinants of suppliers’ bidding behavior in procurement auctions for complex IT services, we find results that are consistent with theory. We find that price and quality do not exhibit the classical tradeoff one would expect: quite surprisingly, high quality is associated to low prices. Furthermore, while quality is mainly driven by suppliers’ experience, price is affected more by the scoring rule and by the level of expected competition. These results might suggest that (scoring) auctions fail to appropriately incorporate buyers’ complex price/quality preferences in the tender design.Procurement Auctions, Scoring Rules, IT Contracts, Price/Quality Ratio

On some collusive and signaling equilibria in ascending auctions for multiple objects

We consider two ascending auctions for multiple objects: the SEAMO (simultaneous English auction for multiple objects) and the the JAMO (Japanese auction for multiple objects). We first derive a (competitive) Perfect Bayesian Equilibrium of the JAMO by exploiting the strategic equivalence between the JAMO and the Survival Auction which consists of a finite sequence of sealed-bid auctions. Then, we prove that many of the (unwanted) collusive or signaling equilibria studied in the literature in the framework of the SEAMO do not have a counterpart in the JAMO. However, it is shown that certain collusive equilibria based on retaliatory strategies do exist in both auctions.Multi-unit auctions; Ascending auctions; FCC auctions; Collusion; Retaliation