Multi-unit demand auctions with synergies: behavior in sealed-bid versus ascending-bid uniform-price auctions

We construct a relatively simple model of bidding with synergies and solve it for both open outcry and sealed-bid uniform-price auctions. The essential behavioral forces involved in these auctions are: (1) A demand reduction force resulting from the monopsony power that bidders with multiple-unit demands have when synergies are relatively inconsequential, and (2) Bidding above stand-alone values in order to capture significant complementarities between units. The latter creates a potential “exposure problem,” as bidders may win only parts of a package and earn negative profits. Bidding outcomes are closer to equilibrium in clock compared to sealed-bid auctions. However, there are substantial and systematic deviations from equilibrium, with patterns of out-of-equilibrium play differing systematically between the two auction formats. These patterns of out-of-equilibrium play are analyzed, along with their effects on revenue and efficiency.     

Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.     

Multi-unit demand auctions with synergies: behavior in sealed-bid versus ascending-bid uniform-price auctions

We construct a relatively simple model of bidding with synergies and solve it for both open outcry and sealed-bid uniform-price auctions. The essential behavioral forces involved in these auctions are: (1) A demand reduction force resulting from the monopsony power that bidders with multiple-unit demands have when synergies are relatively inconsequential, and (2) Bidding above stand-alone values in order to capture significant complementarities between units. The latter creates a potential “exposure problem,” as bidders may win only parts of a package and earn negative profits. Bidding outcomes are closer to equilibrium in clock compared to sealed-bid auctions. However, there are substantial and systematic deviations from equilibrium, with patterns of out-of-equilibrium play differing systematically between the two auction formats. These patterns of out-of-equilibrium play are analyzed, along with their effects on revenue and efficiency.     

Expected revenue of all-pay and first-price sealed-bid auctions with affiliated signals

In the general symmetric auction framework of Milgrom and Weber (1982) it is shown—as a new manifestation of thelinkage principle—that the all-pay sealed-bid auction yieldshigher expected revenue than the standard first-price sealed-bid auction. This raises the question why sealed-bid auctions of the standard first-price variety are observed in practice whereas the all-pay variety is not.     

An experimental investigation of entry cost effects in sealed-bid dollar auctions

We experimentally study the effect of entry costs on bidding and entry behavior in common value auctions. We find, with entry costs, players bid lower in first price and higher in second price auctions, compared to no entry fee auctions.     

First-price sealed-bid auctions when bidders exhibit different attitudes toward risk

When bidders have different risk aversion levels, we determine in a first-price auction, the asymmetric equilibrium strategies. We analyze the impact of asymmetric risk aversion levels on bidders’ markups and on the expected revenue and allocative efficiency of the auction.     

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.     

Informational limitations of ascending combinatorial auctions

We study the inherent limitations of natural widely-used classes of ascending combinatorial auctions. Specifically, we show that ascending combinatorial auctions that do not use both non-linear prices and personalized prices cannot achieve social efficiency with general bidder valuations. We also show that the loss of efficiency can be severe and that only a diminishing fraction of the social welfare may be captured. This justifies the added complexity in the auctions suggested by, e.g., Parkes and Ungar (2000) [29] and Ausubel and Milgrom (2002) [2].     

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.     

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.     

Counting combinatorial choice rules

I count the number of combinatorial choice rules that satisfy certain properties: Kelso–Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties. The rules are a small, and asymptotically vanishing, fraction of all choice rules. But they are still exponentially more than the preference relations over individual agents—which has positive implications for the Gale–Shapley algorithm of matching theory.     

Revenues in discrete multi-unit, common value auctions: a study of three sealed-bid mechanisms

This paper proposes a discrete bidding model for both quantities and pricing. It has a two-unit demand environment where subjects bid for contracts with an unknown redemption value, common to all bidders. Prior to bidding, the bidders receive private signals of information on the (common) value. The relevant task is to compare the equilibrium strategies and the seller’s revenue of the three most common auction formats with two players. The result is that the Vickrey auction always gives the most revenue to the seller, the discriminatory auction follows closely and the uniform auction clearly is the worst due to demand reduction.

Open vs. sealed-bid auctions: testing for revenue equivalence under Singapore's vehicle quota system

Using data from the auction of vehicle quota licenses in Singapore, we study if revenue equivalence holds when the auction format was switched from a sealed-bid format (May 1990 to June 2001) to an open bidding format since July 2001. Our econometric analysis indicates the change in auction format led to a change in bidding behavior. On average, the quota license premium under the open bidding format is about US$1000 (about 7.5% of the Category E license price in June 2001) lower, compared to the forecast level that would have prevailed if there had been no change in the auction format.     

Multi-dimensional reference-dependent preferences in sealed-bid auctions – How (most) laboratory experiments differ from the field

We study bidding behavior in first- and second-price sealed-bid auctions with loss-averse agents. Our model predicts overbidding in first-price induced-value auctions consistent with evidence from most laboratory experiments. Substantially different bidding behavior could result in commodity auctions where money and auction item are consumed along different dimensions of the consumption space. Differences also result in second-price auctions. Our study thereby indicates that transferring qualitative behavioral findings from induced-value laboratory experiments to the field may be problematic if subjects are loss-averse.     

Shadow pricing with suboptimal policy rules

This paper aims to clarify different views on the validity of the little-Mirrlees border price rule for project evaluation in a context where the Government chooses its controls suboptimally in a systematic fashion. The rule is shown to be valid quite generally for small public sector projects when the Government's response restores market-clearing in nontradeables and foreign exchange. It can be invalid in contexts of (a) non-market clearing or (b) private sector projects that generate profits distributed to households. In the latter case special treatment of profit effects is required, along the lines described by Little and Mirrlees (1974).     

Transfer pricing rules and corporate tax competition

A multinational parent sells a non-marketed commodity to a foreign subsidiary that uses the product as an input to produce a product it then sells. The subsidiary is controlled by a local managing partner whose compensation consists of a lump-sum payment plus a share of the subsidiary's profit. The parent chooses an optimal transfer price taking into account incentives for the subsidiary's managing partner and taxes. Home and host governments impose corporate income taxes on the parent and subsidiary's respective profits subject to a transfer pricing rule (e.g. cost plus price method or comparable profit method). A Nash equilibrium is derived for effective tax rates chosen by home and host governments. We then examine harmonization and suggest that tax rates would be reduced.     

On marginal cost pricing with given tax-subsidy rules

We provide an existence proof for Generalized Marginal Cost Pricing with given tax-subsidy rules. The novelty is that our approach allows for economic environments where all the generalized marginal cost pricing equilibria are inefficient in the aggregate. An example is recalled in order to suggest how non-pathological these environments are.     

The interaction of equity and efficiency factors in optimal pricing rules

Operational rules for setting optimal prices for the products of nationalized or regulated industries when both the distribution of income and efficiency are taken into account have been developed. In this paper we look closely at the interaction between equity and efficiency in these rules, in particular at the fact that the terms relating to each will generally be interconnected. When this relationship is taken into account quite simple operational parametric formulations for the optimal pricing rules can be derived and discussed.     

Exploring consumption-based asset pricing model with stochastic-trend forcing processes

Using Canadian data, the consumption-based asset pricing model is studied, defined in terms of nondurable and durable goods consumption. A two-stage estimation procedure is used, which takes account of the presence of common stochastic trends in the forcing processes. This method yields more reasonable estimates of the preference parameters than the previous studies did, and the asset-pricing equation is not rejected by the data. Moreover, the preference specification adopted in this paper allows a number of useful economic information to be obtained. The additive separability assumption and the Cobb–Douglas functional form of the utility function are ruled complements in the sense of Edgeworth and Pareto.