Truthful approximation mechanisms for restricted combinatorial auctions

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness).We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios.     

Bribing in first-price auctions: Corrigendum

We clarify the sufficient condition for a trivial equilibrium to exist in the model of Rachmilevitch (2013).     

Vickrey auctions with reserve pricing

Summary. We generalize the Vickrey auction to allow for reserve pricing in a multi-unit auction with interdependent values. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders' reports of private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings with perfect resale, the Vickrey auction with reserve pricing maximizes seller revenues.Received: 31 December 2002, Revised: 5 May 2003, JEL Classification Numbers: D44, C78, D82.Correspondence to: Lawrence M. AusubelThe authors gratefully acknowledge the generous support of National Science Foundation Grants SES-97-31025, SES-01-12906 and IIS-02-05489. We appreciate valuable comments from Ilya Segal. Special thanks go to Mordecai Kurz, who served as Larry's dissertation advisor and who introduced both authors to the economics profession back at IMSSS at Stanford. Congratulations and best wishes are extended to Mordecai and his family on the happy occasion of the publication of Assets, Beliefs, and Equilibria in Economic Dynamics: Essays in Honor of Mordecai Kurz, in which this article also appears.     

Collusion in one-shot second-price auctions

Summary. Most of the literature on collusive behavior in auctions ignores two important issues that make collusion difficult to sustain at least in one-shot interactions: the detection of cheating and the verification of bids. Colluding bidders may deceive each other by using shill bidders. Also, if the identities of the bidders and their bids are not published then it would be difficult to verify the bid of a colluding bidder. This paper addresses these problems in one shot second price auctions where one bidder offers another bidder a side payment in exchange for not participating in the auction, while the number of other bidders is stochastic. In spite of the barriers to collusion mentioned above, a simple side payment mechanism which depends only on the auction price is introduced. It induces a successful collusion, eliminates the verification problem, provides no incentive for the use of shill bidders and guarantees that the proponent obtains ex-post non-negative payoff. The colluding bidders are ex-ante strictly better off compared with the competitive case, irrespective of their types.Received: 27 November 2002, Revised: 28 January 2005, JEL Classification Numbers: C72, D44, D82.Yair Tauman: Correspondence toWe would like to thank an anonymous referee for very valuable comments and suggestions that significantly improved the paper. We thank Shmuel Zamir for a helpful discussion.     

Second chance offers versus sequential auctions: theory and behavior

Second chance offers in online marketplaces involve a seller conducting an auction for a single object and then using information from the auction to offer a losing bidder a take-it-or-leave-it price for another unit. We theoretically and experimentally investigate this practice and compare it to two sequential auctions. We show that the equilibrium bidding strategy in the second chance offer mechanism only exists in mixed strategies, and we observe that this mechanism generates more profit for the auctioneer than two sequential auctions. We also observe virtually no rejections of profitable offers in the ultimatum bargaining stage.      

Late and multiple bidding in second price Internet auctions: Theory and evidence concerning different rules for ending an auction

In second price Internet auctions with a fixed end time, such as those on eBay, many bidders submit their bids in the closing minutes or seconds of an auction. We propose an internet auction model, in which very late bids have a positive probability of not being successfully submitted, and show that late bidding in a fixed deadline auction can occur at equilibrium in auctions both with private values and with uncertain, dependent values. Late bidding may also arise out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of late bidding are severely attenuated in auctions that apply an automatic extension rule such as auctions conducted on Amazon. Field data show that there is more late bidding on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding.     

Competition in the economic crisis: Analysis of procurement auctions

We study the effects of the recent economic crisis on firms׳ bidding behavior and markups in sealed bid auctions. Using data from Austrian construction procurements, we estimate bidders׳ construction costs within a private value auction model. We find that markups of all bids submitted decrease by 1.5 percentage points in the recent economic crisis, markups of winning bids decrease by 3.3 percentage points. We also find that without the government stimulus package this decrease would have been larger. These two pieces of evidence point to pro-cyclical markups.     

Ranking asymmetric auctions: Filling the gap between a distributional shift and stretch

I consider first-price auctions (FPA) and second-price auctions (SPA) with two asymmetric bidders. The FPA is known to be more profitable than the SPA if the strong bidder's distribution function is convex and the weak bidder's distribution is obtained by truncating or horizontally shifting the former. In this paper, I employ a new mechanism design result to show that the FPA remains optimal if the weak bidder's distribution falls between the two benchmarks in a natural way. The same conclusion holds if the strong bidder's distribution is concave, but with a vertical shift replacing the horizontal shift. A result with a similar flavor holds if the strong bidder's distribution is neither convex nor concave. The dispersive order and the star order prove useful in comparing the weak bidder's distribution to the benchmarks. A key step establishes a relationship between these orders and reverse hazard rate dominance.     

Bundling decisions for selling multiple objects

Summary. Auctioneers often face the decision of whether to bundle two or more different objects before selling them. Under a Vickrey auction (or any other revenue equivalent auction form) there is a unique critical number for each pair of objects such that when the number of bidders is fewer than that critical number the seller strictly prefers a bundled sale and when there are more bidders the seller prefers unbundled sales. This property holds even when the valuations for the objects are correlated for a given bidder. The results have been proved using a mathematical technique of quantiles that can be extremely useful for similar analysis. Received: November 5, 1996; revised version: January 21, 1998     

A study of zero-out auctions: testbed experiments of a process of allocating private rights to the use of public property

Summary This paper applies an experimental testbed methodology to the evaluation of a proposed mechanism for allocating the right to land at the New York airports. The mechanism is called a zero-out auction because it is supposed to allocate the rights efficiently like an auction while leaving all of the consumer's surplus with the buyers (as opposed to allocating some to the seller as would be the case with an ordinary auction). A new behavioral hypothesis is introduced to account for limited rationality of individuals and unusual behaviors of the process. The axiom, called theunbiased expectations hypothesis, does a good job of modeling individual behavior in the context of a game model.We acknowledge the financial support of the National Science Foundation and the Caltech Laboratory for Experimental Economics and Political Science. Comments by David Grether, John Ledyard, Michael Levine, Jennifer Reinganum, and Richard Sutch have been very helpful.     

Dominant design or multiple designs: the flash memory card case

Literature suggests that in battles between competing designs, ultimately one design will emerge as dominant to the detriment of the others. Various factors and forces have been identified to explain this phenomenon. Yet, sometimes no dominant design emerges at all and multiple competing designs coexist in the market. The flash memory card industry provides an example of this. In this study, we use this example as a case to investigate the circumstances under which an industry has a tendency toward multiple designs. The case shows that a combination of factors may result in multiple designs and we argue that such a combination of factors will increasingly also apply in other cases.     

Computerization,workplace organization,skilled labour and firm productivity: Evidence for the Swiss business sector

The present study explores empirically the hypothesis that information and communication technologies, new organizational practices and human capital are important determinants of firm efficiency and performance, further that the combined use of these three factors leads to a mutual strengthening of their impact on firm performance. The analytical framework is that of a production function at firm level. The new contribution of this study to the empirical literature is that it is the first empirical study of this type for the Swiss business sector, using a rich data set at firm level for the year 1999 which were collected by means of a postal survey, and giving particular attention to the complementarity issue (several approaches) and to the endogenization of the technology and organization variables.     

Determining damages from the operation of bidding rings: An analysis of the post-auction `knockout' sale

Summary. This paper studies ‘knockout’ auctions, typically organized by bidding rings, in which the winning bidder makes side-payments to all losing bidders. These side-payments provide an incentive for the ring members to bid higher than they would have in an identical public auction. As a consequence, neither the realized price nor the total payments of the winner are unbiased estimates of the item's price in the absence of collusion. This paper evaluates the extent of this overestimate in the independent private values case, for first and second price post-auction knockouts. Bids are not independent of the sharing rule but transfers from the winning bidder are. Further, bidder payoffs are independent of both the auction format and the sharing rule. The “overbidding” in the knockout is increasing with the dispersion of bidder valuations and of significant empirical relevance. This paper's results can be used to obtain an unbiased assessment of the damages inflicted on the seller. Received: May 1, 1996; revised version: September 7, 2000     

Auctions with endogenous valuations: the snowball effect revisited

Summary. This paper looks at the determination of ownership of capacity when there are two ex-ante symmetric agents bidding for many units of capacity which are sold sequentially. It is shown that convexity of payoffs in the final stage of the game is sufficient to ensure monopolization of capacity, but that increasing returns to scale are not sufficient to ensure monopolization. Received: March 14, 1997; revised version: December 1, 1997     

Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

Priced on the note: the case of Japanese IPOs

ABSTRACT

This article examines the pricing of Japanese IPOs: 54.26% are priced in 1,000 Japanese yen increments (The Japanese yen (JPY) has denominations of banknotes and coins. Banknotes are in 1,000, 2,000, 5,000, and 10,000-yen. Coins are in 1, 5, 10, 50, 100, and 500-yen. One thousand banknotes are similar to US $10 dollars. Coins are considered as changes in Japan.) (note-ending IPOs), an economically large increment on a per-share basis that is equivalent to 10 US dollar increments assuming an exchange rate of 1 US dollar to 100 Japanese yen. The number of note-ending IPOs increases with price levels and pricing uncertainty, supporting the negotiation hypothesis. Note-ending IPOs are associated with higher volatility, higher underwriters’ fees, wider filing price range, smaller deal size, shorter firm age, and lower underwriter reputation. Price clustering contributes to IPO underpricing. The initial returns are 60.44% higher for note-ending relative to coin-ending IPOs. These results shed light on the pricing of Japanese IPOs due to negotiations and on investment opportunities with note-ending IPOs.     

The law of small numbers: investigating the benefits of restricted auctions for public procurement

A commonly accepted view in the academic literature is that dispensing with competition may only be beneficial when tendering complex contracts. However, restricted auctions are frequently used among EU member states to procure small contracts. In this article, we investigate this paradox. Using an original data set of 180 contracts used by a local public buyer of social housing between 2006 and 2009, we show that limiting competition may enable economies to be made on transaction costs while the most efficient bidders still come forward, and that abuses such as corruption or favouritism do not result. To our knowledge, this article is the first to shed light on the advantages of using restricted auctions when tendering small simple contracts.