Optimal auctions for asymmetrically budget constrained bidders

We consider an environment with a single divisible good and two bidders. The valuations of the bidders are private information but one bidder has a commonly known budget constraint. For this environment we derive the revenue maximizing subsidy free dominant strategy incentive compatible auction.      

Evidence of liquidity constraints found in theme park ticket auctions

Data from Internet auctions of unused tickets to Walt Disney World are used to establish the presence and financial impact of liquidity constraints for consumers, even when those consumers are confronted with a very short time horizon and a substantial potential monetary saving. Bidding for tickets is found to be consistent with the microeconomic consumer theory of risk and liquidity. The presence of liquidity premiums and premiums paid for variety in entertainment are separately established. The authors wish to thank an anonymous referee for very helpful comments and would like to acknowledge Michael Toma, Andy Weinbach, and conference participants of the Academy of Economics and Finance.     

Inferring welfare maximizing treatment assignment under budget constraints

This paper concerns the problem of allocating a binary treatment among a target population based on observed covariates. The goal is to (i) maximize the mean social welfare arising from an eventual outcome distribution, when a budget constraint limits what fraction of the population can be treated and (ii) to infer the dual value, i.e. the minimum resources needed to attain a specific level of mean welfare via efficient treatment assignment. We consider a treatment allocation procedure based on sample data from randomized treatment assignment and derive asymptotic frequentist confidence interval for the welfare generated from it. We propose choosing the conditioning covariates through cross-validation. The methodology is applied to the efficient provision of anti-malaria bed net subsidies, using data from a randomized experiment conducted in Western Kenya. We find that subsidy allocation based on wealth, presence of children and possession of bank account can lead to a rise in subsidy use by about 9% points compared to allocation based on wealth only, and by 17% points compared to a purely random allocation.     

Capacity constraints and the winner's curse in multi-unit common value auctions

We explore the role of capacity constraints in establishing efficient pricing in multi-unit common value auctions in a setting relevant to auction-based equity IPOs. The method of inquiry is experimental economics. We find that sufficiently large capacity constraints mitigate the overbidding that plagues single-unit auctions and is one of the most robust laboratory findings. We also uncover a puzzling propensity for most bidders to place a portion of their bids at prices above their signals. This disequilibrium behavior persists with experience and in cases with substantial losses in previous auctions. Our results suggest caution is warranted in promoting auction based IPOs that allow unrestricted access by the non-professional investing public.     

Nonlinear budget constraints and consumer demand: An application to public programs for residential housing

This study presents a methodology for exploiting the nonlinear hedonic nature of housing prices to estimate the compensated demands of households for particular housing attributes. The methodology is employed to provide Hicksian benefit measures of a particular housing subsidy program typical of those undertaken recently in developing countries.     

Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints

We analyze the nonlinear pricing problem faced by an incomplete information monopolist operating in a market populated by agents with budget constraints. We show that if other goods are available and if the monopolist's goods are nonessential relative to other goods, then there exists an optimal, individually rational, and incentive compatible selling mechanism for the monopolist (Theorem 1). Moreover, we show that a solution to all such nonlinear pricing problems exists if and only if the monopolist's goods are nonessential (Theorem 2). In the absence of nonessentiality, we show that if the monopolist's profit function is independent of quantity (e.g., if all costs are fixed), then an optimal selling mechanism exists (Theorem 3). Finally, we show that if there is reporting (of types by agents) and partial recognition of types (by the monopolist), then an optimal selling mechanism exists, even in the absence of nonessentiality, provided agents' utility functions are affine and continuous in goods (Theorem 4).     

Optimal two-object auctions with synergies

We design the revenue-maximizing auction for two objects when each buyer has bi-dimensional private information and a superadditive utility function (i.e., a synergy is generated if a buyer wins both goods). In this setting the seller is likely to allocate the objects inefficiently with respect to an environment with no synergies (see Armstrong, RES (2000)). In particular, the objects may be bundled too rarely or a buyer may win the bundle even though her valuations for the goods are weakly dominated by the values of another buyer.Received: 29 October 2001, Accepted: 29 October 2002, JEL Classification: D44, D82This paper has been written while the author was a member of the Dipartimento di Statistica e Matematica Applicata alle Scienze Umane "Diego De Castro", Universitá degli Studi di Torino, Italy. Valuable comments and suggestions were provided by Antonio Cabrales, Massimo Marinacci, three anonymous referees and, especially, by Mark Armstrong. The usual disclaimer applies.     

Common value auctions with independent types

In this paper I consider a common value model, with independent types, where the ex-post value of the good is influenced by the bidders' information at the auction stage. The seller cannot fully extract the surplus. In a symmetric model the optimal mechanism can be implemented through first price, second price, or English auctions; but not through a Dutch auction. Other properties of the optimal auctions are that the seller's reservation price is endogenous, and that in sealed bid auctions the price may exceed the value of the object (winner's curse).     

Implementing optimal procurement auctions with exogenous quality

In this paper, we consider the implementation of the optimal procurement auction outcome when there is a trade-off between price and quality for the buyer. The quality proposals of the competing firms are assumed to be exogenous and common knowledge. After defining the optimal auction, we characterize the discriminatory first score auction and the modified second score auction implementing it when the buyer is assumed to have the same information as the firms. Then we consider an auction which requires no specific information from the buyer and show that a second score auction followed by a negotiation stage can implement the optimal auction outcome under this more realistic assumption. Received: 30 March 2001 / Accepted: 14 December 2001 I am grateful to the anonymous referees for comments on an earlier version of this paper. The usual disclaimer applies.     

The condominium problem; auctions for substitutes

This paper considers the problem of designing selling procedures for substitutes (like condominium units). Oral, ascending auctions for the right to choose are efficient. This is a common type of auction used for the sale of real estate. Efficiency is not optimal from the seller’s viewpoint. An optimal procedure distorts the right-to-choose auction to favor in late rounds bidders whose preferred object has already been sold. This optimal auction is complex. A revenue improving departure from efficiency can be achieved by simply auctioning all the rights to choose before any of them is exerted.Received: 5 February 2003, Accepted: 15 February 2005, JEL Classification: D44I acknowledge very helpful comments by Joe Harrington, Ken Hendricks, and anonymous referees. Financial aid from the European Commission through the TMR Program (contract FMRX-CT98-0203) and the Spanish MCyT (Grants SEC 2002-02506 and SEC 2003-08080) is also gratefully acknowledged.     

The econometrics of auctions with asymmetric anonymous bidders

We consider standard auction models when bidders’ identities are not-or are only partially-observed by the econometrician. We first adapt the definition of identifiability to a framework with anonymous bids and explore the extent to which anonymity reduces the possibility of identifying private value auction models. Second, in the asymmetric independent private value model which is nonparametrically identified, we generalize Guerre, Perrigne and Vuong’s estimation procedure [Optimal nonparametric estimation of first-price auctions, Econometrica 68 (2000) 525-574] and consider the asymptotic properties of our multi-step kernel-based estimator. Monte Carlo simulations illustrate the practical relevance of our estimation procedure in small data sets.     

Identification of first-price auctions with non-separable unobserved heterogeneity

We propose a novel methodology for identification of first-price auctions, when bidders’ private valuations are independent conditional on one-dimensional unobserved heterogeneity. We extend the existing literature ( and ) by allowing the unobserved heterogeneity to be non-separable from bidders’ valuations. Our central identifying assumption is that the distribution of bidder values is increasing in the state. When the state-space is finite, such monotonicity implies the full-rank condition needed for identification. Further, we extend our approach to the conditionally independent private values model of Li et al. (2000), as well as to unobserved heterogeneity settings in which the implicit reserve price or the cost of bidding varies across auctions.     

Preemptive bidding in takeover auctions with affiliated values

This paper extends Fishman's (1988) model of preemptive bidding in takeover auctions to auctions with affiliated values. It shows that preemptive bidding transfers wealth from the seller to the first bidder without affecting the profit of the second bidder and social welfare. It also shows that higher correlation between bidders’ values leads to higher preemption rates but has an ambiguous effect on the size of the opening bid. Finally, it shows that in auctions with affiliated values, even infinitesimal entry costs may lead to a preemptive jump bidding that allows the reallocation of the entire surplus from the seller to the first bidder.     

Core-stable rings in second price auctions with common values

In a common value auction in which the information partitions of the bidders are connected, all rings are core-stable. More precisely, the ex ante expected utilities of rings, at the (noncooperative) sophisticated equilibrium proposed by Einy et al. [Einy, E., Haimanko, O., Orzach, R., Sela, A., 2002. Dominance solvability of second-prices auctions with differential information. Journal of Mathematical Economics 37, 247–258], describe a cooperative games in characteristic function form, in spite of the underlying strategic externalities. A ring is core-stable if the core of this characteristic function is not empty. Furthermore, every ring can implement its sophisticated equilibrium strategy by means of an incentive compatible mechanism. An example shows that, if the bidders’ information partitions are not connected, rings may no longer be core-stable.     

Optimal auctions under collusion of buyers with discrete valuations

The potential seller of an indivisible good faces two potential buyers whose valuations for the good are private information. We derive the optimal selling mechanism under the assumption that the buyers collude both when the valuations are independently distributed and when they are correlated. We find that when the valuations are independent the seller can obtain the same expected revenue as if the buyers behaved noncooperatively; if instend the valuations are correlated then collusion harms the seller. In this latter case, moreover, each buyer’s information at the collusion stage about the other buyer’s valuation turns out to be very relevant for the effectiveness of collusion.     

Wars of attrition and all-pay auctions with stochastic competition

We extend the war of attrition and all-pay auction analysis of Krishna and Morgan (1997) to a stochastic competition setting. We determine the existence of equilibrium bidding strategies and discuss the potential shape of these strategies. Results for the war of attrition contrast with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Furthermore we investigate the expected revenue comparisons among the war of attrition, the all-pay auction and the winner-pay auctions and discuss the linkage principle as well. Our findings are applicable to future works on contests and charity auctions.     

Optimal auctions with multidimensional types and the desirability of exclusion

Within the context of a single-unit, independent private values auction model, we show that if bidder types are multidimensional, then under the optimal auction exclusion of a positive measure of bidder types occur. The results complements Armstrong’s (1996) exclusion of types result.     

Organizational design with a budget constraint

In this paper we point out that the presence of the budget constraint substantially affects the relative performance of organizational decision rules. For instance, if there are only two types of projects to decide upon, the hierarchy always performs better than the polyarchy. The same result holds for any distribution of the quality of projects. We also illustrate that optimal mechanisms for variable evaluation costs involve stopping rules which look hierarchical, but avoid costly duplication as in hierarchies or polyarchies. Received: 5 November 1995 / Accepted: 18 September 1997     

Soft budget constraints and strategic interactions in subnational borrowing: Evidence from the German States, 1975-2005

Cooperative federations are usually characterized by the existence of bailout guarantees and intergovernmental transfer schemes. This paper explores whether such features of cooperative federations lead to subnational soft budget constraints using panel data from the German States covering the 1975-2005 period. The methodology is based on the premise that subnational governments’ borrowing will exhibit vertical and horizontal strategic interactions if they operate under soft budget constraints. Therefore, a test for strategic interactions in subnational borrowing can be used to infer whether a cooperative federation like Germany is susceptible to soft budget constraints. The results suggest that state borrowing in Germany exhibited horizontal but not vertical interactions during the time-frame of the analysis. This indicates (i) that German States faced soft budget constraints and (ii) that they were more concerned about the likelihood of a bailout than about its volume.