Premium auctions and risk preferences

In a premium auction, the seller offers some “payback”, called premium, to a set of high bidders at the end of the auction. This paper investigates how the performance of such premium tactics is related to the bidders? risk preferences. We analyze a two-stage English premium auction model with symmetric interdependent values, in which the bidders may be risk averse or risk preferring. Upon establishing the existence and uniqueness of a symmetric equilibrium, we show that the premium causes the expected revenue to increase in the bidders? risk tolerance. A “net-premium effect” is key to this result.     

English auctions with resale: An experimental study

I design and test a simple English auction and two English auctions with resale, but with different informational backgrounds. All three treatments theoretically have the same equilibrium. I find, however, that the possibility of resale alters behavior significantly. In the two treatments with resale, subjects deviated from both the Nash prediction and the common results about bidding behavior in English auctions. Subjects tend to overbid, when they are certain they can reap the whole surplus in the resale market. I employ different models like QRE and levels of reasoning and conclude that overbidding can be explained as a rational response to the noisy environment in markets with human participants, that is, as rational decision making when anticipating others to make errors. When the outcome of the resale market is not certain, there is significant signaling behavior and auction prices tend to be lower than the Nash prediction.     

Sequential auctions with randomly arriving buyers

We analyze a dynamic market in which buyers compete in a sequence of private-value auctions for differentiated goods. New buyers and new objects may arrive at random times. Since objects are imperfect substitutes, buyers? values are not persistent. Instead, each buyer?s private value for a new object is a new independent draw from the same distribution.We consider the use of second-price auctions for selling these objects, and show that there exists a unique symmetric Markov equilibrium in this market. In equilibrium, buyers shade their bids down by their continuation value, which is the (endogenous) option value of participating in future auctions. We characterize this option value and show that it depends not only on the number of buyers currently present on the market and the distribution of their values, but also on anticipated market dynamics.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

Core-stable rings in auctions with independent private values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders? final utility possibly depends on the winner?s identity. We show that such direct externalities offer a possible explanation for cartels? structures (not) observed in practice.     

Axioms for minimax regret choice correspondences

This paper unifies and extends the recent axiomatic literature on minimax regret. It compares several models of minimax regret, shows how to characterize the according choice correspondences in a unified setting, extends one of them to choice from convex (through randomization) sets, and connects them by defining a behavioral notion of perceived ambiguity. Substantively, a main idea is to behaviorally identify ambiguity with failures of independence of irrelevant alternatives. Regarding proof technique, the core contribution is to uncover a dualism between choice correspondences and preferences in an environment where this dualism is not obvious. This insight can be used to generate results by importing findings from the existing literature on preference orderings.     

Treasury auctions in Spain: a linear approach

Abstract. The majority of Treasuries use discriminatory auctions to sell government debt. A few Treasuries use uniform auctions. The Spanish Treasury is the only one that uses a hybrid format of discriminatory and uniform auctions. All Treasury auctions are multiple-unit multiple-bid auctions, usually assumed to be common and unknown value auctions. Taking in account these features, we analyze the Spanish auction format, taking a linear approximation to bidders' multiple bids, and characterize a parameter set in which the Spanish format gives higher expected seller's revenue than discriminatory and uniform auctions. Policy implications are obtained by calibrating theoretical results with data. We thank S. Nu?ez, and seminar participants at GREQAM, CEFI, the 1999 CEF meeting in Boston and the 57th European Meeting of the Econcometric Society for suggestions. We are especially grateful to two anonymous referees for detailed comments that greatly improved the paper. Any error is our responsability. The authors express their thanks for financial support to Ministerio de Ciencia y Teconologia from Proyecto SEC2000-0723, n_o 9114.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent?s consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent?s income realized to date. We characterize this function in terms of the agent?s outside option value function and the discounted amount of time in which the agent?s income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez–Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley–Aiyagari incomplete-markets models.     

Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210–217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210–217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247–1258] as one in which agents hold private information about the informativeness of their signals about other agents? types. Instead, such an interpretation is warranted only when the weights used to span an agent?s set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.     

Nonmanipulable Bayesian testing

This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, as long as uninformed experts do not learn the correct forecasts too quickly, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on some data-generating processes; however, the set of such processes is topologically small. These results contrast sharply with many negative results in the literature.     

Optimal stopping with dynamic variational preferences

We solve optimal stopping problems in uncertain environments for agents assessing utility by virtue of dynamic variational preferences as in Maccheroni, Marinacci and Rustichini (2006) [16] or, equivalently, assessing risk in terms of dynamic convex risk measures as in Cheridito, Delbaen and Kupper (2006) [4]. The solution is achieved by generalizing the approach in Riedel (2009) [21] introducing the concept of variational supermartingales and variational Snell envelopes with an accompanying theory. To illustrate results, we consider prominent examples: dynamic multiplier preferences and a dynamic version of generalized average value at risk introduced in Cheridito and Tianhui (2009) [5].     

Multiple unit auctions with strategic price-quantity decisions

Summary. I study a multiple unit auction where symmetric risk-neutral bidders choose prices and quantities endogenously. In the model, bidders (a) may place non-linear valuations on the auctioned units, and (b) bid for several units at the same price (“lumpy” bids). I characterize quantity-symmetric and strictly monotone-increasing price equilibria for discriminatory and competitive auctions, and show that (i) if quantity strategy profiles are equal across auctions revenue- equivalence holds, (ii) expected revenue is higher if bidders bid for the entire supply rather than for shares of it, and (iii) equilibrium allocations may fail to be Pareto-optimal. Received: April 14, 1995; revised version: September 3, 1997     

A dynamic model of unsecured credit

We study the terms of credit in a competitive market in which sellers (lenders) are willing to repeatedly finance the purchases of buyers (borrowers) by engaging in a credit relationship. The key frictions are: (i) the lender cannot observe the borrower?s ability to repay a loan; (ii) the borrower cannot commit to any long-term contract; (iii) it is costly for the lender to contact a borrower and to walk away from a contract; and (iv) transactions within each credit relationship are not publicly observable. The lender?s optimal contract has two key properties: delayed settlement and debt forgiveness. Finally, we study the impact of changes in the initial cost of lending on the contract terms.     

The robustness of robust implementation

We show that a mechanism that robustly implements optimal outcomes in a one-dimensional supermodular environment continues to robustly implement ε-optimal outcomes in all close-by environments. Robust implementation of ε-optimal outcomes is thus robust to small perturbations of the environment. This is in contrast to ex-post implementation which is not robust in this sense as only trivial social choice functions are ex-post implementable in generic environments.     

Rents, military elites, and political democracy

In autocratic regimes the military elite is in a position to extract rents, because without the support of the military the government is in general not able to sustain itself. In this paper, we empirically confirm the negative relation between transfers to the military and the degree of democracy for developing countries. We use an instrumental variable approach to account for the simultaneity that arises since the degree of democracy is itself a function of transfers to the military.     

Optimal search auctions

We study the design of profit maximizing single unit auctions under the assumption that the seller needs to incur costs to contact prospective bidders and inform them about the auction. With independent bidders’ types and possibly interdependent valuations, the seller's problem can be reduced to a search problem in which the surplus is measured in terms of virtual utilities minus search costs. Compared to the socially efficient mechanism, the optimal mechanism features fewer participants, longer search conditional on the same set of participants, and inefficient sequence of entry.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

Informational size and incentive compatibility with aggregate uncertainty

In McLean and Postlewaite (Econometrica 56, 1992, p. 2421), we analyzed pure exchange economies with asymmetrically informed agents. We defined a notion of informational size and showed that, when the aggregate information of all agents resolves nearly all the uncertainty regarding the state of nature, the conflict between incentive compatibility and (ex post) efficiency can be made small if agents have sufficiently small informational size. This paper investigates the relationship between informational size and efficiency for the case in which nontrivial aggregate uncertainty is present, i.e., when significant uncertainty about the world persists even when the information of all agents is known.     

Multi-unit auctions with uniform prices

Summary. Auctions in which individuals can purchase more than one unit of the good being sold differ in striking ways from multi-unit auctions in which individuals may purchase only one unit. The uniform price auction in particular frequently yields Nash equilibria in which bidders underbid for their second unit and therefore pay very low prices for the good. This paper characterizes equilibria for the uniform price auction. Received: July 31, 1995; revised version: May 28, 1997