Multidimensional private value auctions

We consider parametric examples of symmetric two-bidder private value auctions in which each bidder observes her own private valuation as well as noisy signals about her opponent's private valuation. We show that, in such environments, the revenue equivalence between the first and second price auctions (SPAs) breaks down and there is no definite revenue ranking; while the SPA is always efficient allocatively, the first price auction (FPA) may be inefficient; equilibria may fail to exist for the FPA. We also show that auction mechanisms provide different incentives for bidders to acquire costly information about opponents’ valuation.     

Learning to bid: The design of auctions under uncertainty and adaptation

We examine auction design in a context where symmetrically informed adaptive agents with common valuations learn to bid for a good. Despite the absence of private valuations, asymmetric information, or risk aversion, bidder strategies do not converge to the Bertrand–Nash equilibrium strategies even in the long run. Deviations from equilibrium strategies depend on uncertainty regarding the value of the good, auction structure, the agents? learning model, and the number of bidders. Although individual agents learn Nash bidding strategies in isolation, the learning of each agent, by flattening the best-reply correspondence of other agents, blocks common learning. These negative externalities are more severe in second-price auctions, auctions with many bidders, and auctions where the good has an uncertain value ex post.     

Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Selling an asset to a competitor

A seller decides whether to allocate an item among two potential buyers. The seller and buyer 1 interact ex post in such a way that each of them suffers a negative externality if the other possesses the item. We show that the optimal allocation rule favors buyer 2, who does not interact ex post with the seller, and in particular bidder 1 may not obtain the good even if his valuation is highest. The auction is therefore subject to resale. When resale is possible, the seller must distort the original auction. We show that the mechanism depends crucially on the way resale is organized ex post. The seller may decide to always allocate the good to the agent with the highest valuation when rents are fully extracted by an intermediary on the resale market. However, she may resort to a stochastic mechanism when the winner of the primary auction has full bargaining power in the resale stage.     

The timing of contracting with externalities

This paper endogenizes the timing of bilateral contracting between one principal and multiple agents in the presence of externalities. Contracting simultaneously with all agents is optimal for the principal if externalities become weaker the more an agent trades. If instead externalities become stronger, sequential negotiations might benefit the principal as they lower the agents’ outside options. Under some linearity conditions, the principal's preferences with respect to different timings of contracting are opposed to their efficiency ranking.     

Information structures in optimal auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. We show that an optimal information structure exists.     

An optimal auction for capacity constrained bidders: a network perspective

This paper examines the problem of a seller with limited supply selling to a group of agents whose private information is two-dimensional. Each agent has a constant marginal value for the good up to some capacity, thereafter it is zero. Both the marginal value and the capacity are private information. We describe the revenue maximizing Bayesian incentive compatible auction for this environment. A novel feature of the analysis is an interpretation of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice. We thank the referees for a number of useful suggestions that have been incorporated into the paper. Mallesh Pai suggested the argument given in Lemma 1. The research was supported in part by the NSF grant ITR IIS-0121678.     

Researching Preferences,Valuation and Hypothetical Bias

A number of recent papers in environmental economics have focused on the process of researching preferences – agents are uncertain about preferences but with effort may narrow their uncertainty. This issue has arisen in formulating bids in contingent valuation (CV) as well as the debate over the divergence between WTP and WTA. In the context of CV, it has been suggested that the hypothetical nature of the preference elicitation process biases responses. This paper provides both a theoretical model and experimental evidence to contribute to this debate. The model is a model of competitive bidding for a private good with two components that are particularly relevant to the debate. The first component is that bidders are unsure of their own value for the private good but may purchase information about their own value (researching preferences). The second component is that there is a probability that the auction is hypothetical – that the winning bidder will not get the private good and will not pay the winning bid. The experiment tests this theoretical model of bidding equilibrium and analyzes the effects of variations in the parameters (hypotheticalness, information costs and number of agents) on the endogenous variables (such as the proportion of bidders who become informed and the winning bid). Experimental results suggest that an increase in the hypotheticalness of an auction tends to decrease the likelihood that bidders pay for information on their valuation with an ambiguous effect on the winning bid.      

THE SECOND‐PRICE AUCTION SOLVES KING SOLOMON'S DILEMMA*

The planner wants to give k identical, indivisible objects to the top k valuation agents at zero costs. Each agent knows her own valuation of the object and whether it is among the top k. Modify the (k+ 1)st‐price sealed‐bid auction by introducing a small participation fee and the option not to participate in it. This simple mechanism implements the desired outcome in iteratively undominated strategies. Moreover, no pair of agents can profitably deviate from the equilibrium by coordinating their strategies or bribing each other.     

The Relevance of a Choice of Auction Format in a Competitive Environment

We examine the relevance of an auction format in a competitive environment by comparing uniform and discriminatory price auctions with many bidders in a private values setting. We show that if the number of objects for sale is small relative to the number of bidders, then all equilibria of both auctions are approximately efficient and lead to approximately the same revenue. When the number of objects for sale is proportional to the number of bidders, then the particulars of the auction format matter. All equilibria of the uniform auction are efficient, while all of the equilibria of the discriminatory auction are inefficient. The relative revenue rankings of the auction formats can go in either direction, depending on the specifics of the environment. These conclusions regarding the efficiency and revenue ranking are in contrast to the previous literature, which focused on the case of independent information across agents.     

The effectiveness of English auctions

We study the performance of the English auction under different assumptions about the seller's degree of “Bayesian sophistication.” We define the effectiveness of an auction as the ratio between the expected revenue it generates for the seller and the expected valuation of the object to the bidder with the highest valuation (total surplus). We identify tight lower bounds on the effectiveness of the English auction for general private-values environments, and for private-values environments where bidders' valuations are non-negatively correlated. For example, when the seller faces 12 bidders who the seller believes have non-negatively correlated valuations whose expectations are at least as high as 60% of the maximal possible valuation, an English auction with no reserve price generates an expected price that is more than 80% of the value of the object to the bidder with the highest valuation.     

COMMUNITY PROPERTY AUCTION,NASH BIDDING RULE AND CHINA'S RURAL ECONOMIC REFORM

In this paper we present a model based on the auction theory for community properties and its possible application to China's economic reforms. We derive the Nash bidding rule for the first price sealed‐bid auction of a community‐owned object, and compare it with the bidding rule for auctions of a privately‐owned object. Moreover, we argue that in the process of China's economic reforms, auctioning off the community‐owned properties to private owners is the optimal way to achieve economic efficiency together with social equity. This paper has obvious implications for China's reforms relating to commercializing its rural land and other community property.     

Risk aversion and optimal reserve prices in first- and second-price auctions

We analyze the effects of buyer and seller risk aversion in first- and second-price auctions in the classic setting of symmetric and independent private values. We show that the seller's optimal reserve price decreases in his own risk aversion, and more so in the first-price auction. The reserve price also decreases in the buyers' risk aversion in the first-price auction. Thus, greater risk aversion increases ex post efficiency in both auctions - especially that of the first-price auction. At the interim stage, the first-price auction is preferred by all buyer types in a lower interval, as well as by the seller.     

Bidding up, buying out and cooling-off: an examination of auctions with withdrawal rights

Summary. This paper considers a model in which bidders in an auction are faced with uncertainty as to their final valuation of the auctioned object. This uncertainty is resolved after the auction has taken place. It is argued that the inclusion of a cooling-off right raises the expected revenue to the seller when bidders face a risk of the object being a strict 'bad', in that owning the object incurs negative utility to the winner of the auction. The model is then tested in a laboratory setting. The evidence from this experiment supports the predictions of the theory.     

Valuation structure in first-price and least-revenue auctions: an experimental investigation

In many auctions the valuation structure involves both private and common value elements. Existing experimental evidence (e.g. Goeree and Offerman in Am. Econ. Rev. 92(3):625–643, 2002) demonstrates that first-price auctions with this valuation structure tend to be inefficient, and inexperienced subjects tend to bid above the break-even bidding threshold. In this paper, we compare first-price auctions with an alternative auction mechanism: the least-revenue auction. This auction mechanism shifts the risk regarding the common value of the good to the auctioneer. Such a shift is desirable when ex post negative payoffs for the winning bidder results in unfulfilled contracts, as is often the case in infrastructure concessions contracts. We directly compare these two auction formats within two valuation structures: (1) pure common value and (2) common value with a private cost. We find that, relative to first-price auctions, bidding above the break-even bidding threshold is significantly less prevalent in least-revenue auctions regardless of valuation structure. As a result, revenue in first-price auctions is higher than in least-revenue auctions, contrary to theory. Further, when there are private and common value components, least-revenue auctions are significantly more efficient than first-price auctions.     

Optimal sale across venues and auctions with a buy-now option

We characterize the optimal selling mechanism for a seller who faces demand demarcated by a high and a low end and who can access an (online) auction site (by paying an access cost) in addition to using his own store that can be used as a posted price selling venue. We first solve for the optimal mechanism of a direct revelation game in which there is no venue-restriction constraint. We find that the direct optimal mechanism must necessarily incorporate a certain kind of pooling. We then show that even with the venue constraint, the seller can use a two stage indirect mechanism that implements the allocation rule from the optimal direct mechanism, and uses the venues in an optimal fashion. The first stage of the indirect mechanism is a posted price at the store. If the object is not sold, we move to stage two, which involves an auction at the auction site. A feature of this auction is a buy-now option which is essential for implementing the pooling feature of the optimal direct mechanism. We also show that the buy-now option in the optimal mechanism is of a “temporary” variety, and that a “permanent” buy-now option, in contrast, cannot implement the optimal mechanism. Auctions with a temporary buy-now option are in widespread use on eBay. We thank the Associate Editor, George Deltas, for his insightful comments. We also thank seminar participants at the University of Basel and the SAET conference 2007.     

Water valuation at basin scale with application to western India

A parsimonious hydro-economic model for a data scarce dryland area is presented. It features a basin level decentralized water allocation mechanism which is adapted to incorporate sustainable water use and to deal with the externalities from upstream-downstream linkages. We formulate the profit maximization problem of various agents in a basin, each identifying a sub-basin, who operate within the boundaries of a spatially explicit model that describes the dominant hydrological processes. We address issues of non-convexities and non-steady state conditions and elicit the dependence of a decentralized water allocation on geophysical properties of the basin. In particular, the approach describes how the competition between the drying and drainage functions of sub-basins in dryland areas manifests itself in the optimal valuation of water. The application to an area of over 500,000 km² and 34 sub-basins in western India indicates that intra-basin cooperation could be beneficial; valuation of inter basin flows as a percentage of respective sub-basin income is on an average around 30% when each sub-basin includes downstream valuation as well.     

Environmental degradation as engine of undesirable economic growth via self-protection consumption choices

We analyze growth dynamics in an economy where the well-being of economic agents depends on three goods: leisure, a free access environmental good and a private good that can be consumed as a substitute for the environmental resource. The processes of production and consumption of the private good by each agent impose negative externalities on other agents through the depletion of the environmental good.This paper shows that, in such context, the existence of private substitutes for environmental goods may fuel an undesirable economic growth process. This process is driven by the continuous increase in agents' needs for private consumption generated by the progressive reduction in free consumption of the environmental good.     

Optimal Multi-Object Auctions

This paper analyses optimal auctions of several objects. In the first model bidders have a binary distribution over their valuations for each object, in which case the optimal auction is efficient. The optimal auction takes one of two formats: either objects are sold in independent auctions, or a degree of bundling is introduced in the sense that the probability a bidder wins one object is increasing in her value for the other. The format of the optimal auction may depend upon the number of bidders. In the second model the restriction to binary distributions is relaxed, and the optimal auction is then inefficient.     

Efficient collusion in repeated auctions with communication

This paper studies collusion in repeated auctions when bidders communicate prior to each stage auction. For independent and correlated private signals and general interdependent values, the paper identifies conditions under which an equilibrium collusion scheme is fully efficient in the sense that the bidders’ payoff is close to what they get when the object is allocated to the highest valuation bidder at the reserve price in every period.