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In this paper, we analyze the role of negative prizes in contest design with a fixed budget, risk-neutral contestants, and independent private abilities. The effort-maximizing prize allocation rule features a threshold. When the highest effort is above the threshold, all contestants with lower efforts receive negative prizes. These negative prizes are used to augment the prize to the contestant with the highest effort, which better incentivizes contestants with higher abilities. When no contestant's effort exceeds the threshold, all contestants equally split the initial budget (or a portion of it) to ensure their participation. We find that allowing negative prizes can increase the expected total effort dramatically. In particular, if no bound is imposed on negative prizes, the expected total effort can be arbitrarily close to the highest possible effort inducible when all contestants have the maximum ability with certainty. The above contest is shown to be the optimal mechanism for a more general class of mechanisms.

I consider a broad class of economic environments where a principal contracts with an agent under adverse selection and the agent can credibly disclose information to the principal. I show that there is an equilibrium that interim Pareto dominates the equilibrium without evidence if and only if the optimal mechanism without evidence assigns the outside option to a set of types satisfying a ‘gains from trade’ property. The results apply to a range of economic environments including insurance markets, financial markets and goods markets with quality-based price discrimination.

We study optimal dynamic selling mechanisms in a two-stage model where the buyer can search for a better price at the second stage. When this outside price is public, the optimal selling mechanism takes the form of a fixed first-stage price with price matching in the second stage. In contrast, when the outside price is the buyer's private information, the optimal mechanism is a menu of two contracts: a first-stage sale at a higher price with immediate delivery, or a first-stage sale at a lower price with second-stage delivery. Thus the optimal form of search deterrence depends on the observability of the buyer's outside option.

This paper applies a mechanism design approach to construct a lower bound to the welfare cost of inflation that does not depend on quasi-linear preferences or details of how agents trade. An incentive-feasible trading protocol is derived to minimize the welfare loss subject to frictions rendering money essential. The welfare cost of inflation under this optimal protocol is the lower bound over all pairwise trading protocols of monetary exchange. In general, the first-best is not implementable, even under the Friedman's rule, patient agents and the optimal mechanism. Thus, the lower bound depends on fundamentals like preferences and technology. Finally, I estimate the irreducible cost of 10% inflation with the U.S. data from 1900 to 2000.

A seller maximizes revenue from selling an object in a dynamic environment, with buyers that differ in their patience: Each buyer has a privately known deadline for buying and a privately known valuation. First, we derive the optimal mechanism, neglecting the incentive constraint for the deadline. The deadline of the winner determines the time of the allocation and therefore also the amount of information available to the seller when he decides whether to allocate to a buyer. Depending on the shape of the markup that the seller uses, this can lead to a violation of the neglected incentive constraint. We give sufficient conditions on the type distribution under which the neglected constraint is fulfilled or violated. Second, for the case that the constraint cannot be neglected, we consider a model with two periods and two buyers. Here, the optimal mechanism is implemented by a fixed price in period one and an asymmetric auction in period two. The asymmetry, which is introduced to prevent the patient type of the first buyer from buying in period one leads to pooling of deadlines at the top of the type space.

We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the first-price and second-price auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity.

We characterize revenue maximizing mechanisms in auction settings with ‘rich’ type spaces, where bidders obtain information from sources other than their own valuation. The focus of the paper is on the concept of Bayes-Nash implementation. By considering a relaxed problem, we provide an upper bound on revenue extraction that explicitly builds on the richness of the information structure. We provide a condition under which this upper bound is achieved and characterize a mechanism that does it. Under this condition, we also show that the optimal revenue can be achieved with dominant strategy implementation.The characterization of optimal revenue generalizes the full surplus extraction result of Cremer and McLean (1988) as well as the standard independent private values optimal auction presented in Myerson (1981), providing a unified treatment for two sets of results considered irreconcilable so far.

This paper adopts mechanism design to investigate the coexistence of …at money and higherreturn assets. We consider an economy with pairwise meetings where …at money and riskfree capital compete as means of payment, as in Lagos and Rocheteau (2008). The trading mechanism in pairwise meetings is chosen among all individually rational, renegotiation-proof mechanisms to maximize society’s welfare. We show that in any stationary monetary equilibrium capital commands a higher rate of return than …at money.

In this paper, we examine the optimal mechanism design of selling an indivisible object to one regular buyer and one publicly known buyer, where inter-buyer resale cannot be prohibited. The resale market is modeled as a stochastic ultimatum bargaining game between the two buyers. We fully characterize an optimal mechanism under general conditions. Surprisingly, in this optimal mechanism, the seller never allocates the object to the regular buyer regardless of his bargaining power in the resale market. The seller sells only to the publicly known buyer, and reveals no additional information to the resale market. The possibility of resale causes the seller to sometimes hold back the object, which under our setup is never optimal if resale is prohibited. We find that the sellerʼs revenue is increasing in the publicly known buyerʼs bargaining power in the resale market. When the publicly known buyer has full bargaining power, Myersonʼs optimal revenue is achieved; when the publicly known buyer has no bargaining power, a conditionally efficient mechanism prevails.

I apply mechanism design to quantify the cost of inflation that can be attributed to monetary frictions alone. In an environment with pairwise meetings, the money demand that is consistent with a constrained-efficient allocation takes the form of a continuous correspondence that can fit the data over the period 1900–2006. For such parameterizations, the cost of moderate inflation is zero. This result is robust to different assumptions regarding the observability of money holdings, the introduction of match-specific heterogeneity, and endogeneous participation decisions.

In allocating goods with no use of monetary transfers, random allocation mechanisms can be designed in order to elicit information on preference intensities. I study the nontransfer allocation of two ex-ante identical objects under Bayesian incentive compatibility, with symmetric agents and independent private valuations. I find the ex-ante utilitarian-optimal mechanism, in which the probability of receiving a specified object is used as “numeraire” to purchase probability units of the other object. I characterize this mechanism as an appropriate combination of lotteries, auctions and insurance. The latter element ensures that efficient auctions are feasible. If the problem is constrained to guarantee exactly one object per agent, then the optimal mechanism uses no information other than the agentsʼ ordinal preferences.

This paper studies optimal auction design when the seller can affect the buyersʼ valuations through an unobservable ex ante investment. The key insight is that the optimal mechanism may have the seller play a mixed investment strategy so as to create correlation between the buyersʼ otherwise (conditionally) independent valuations. Assuming that the seller announces the mechanism before investing, the paper establishes conditions on the investment technology so that a mechanism exists which leaves buyers no information rent and leaves the seller indifferent between his investments. Under these conditions, the seller can, in fact, extract the first best surplus almost fully.

In an intertemporal setting in which individual uncertainty is resolved over time, advancepurchase discounts can serve to price discriminate between consumers with different expected valuations for the product. Consumers with a high expected valuation purchase the product before learning their actual valuation at the offered advance-purchase discount; consumers with a low expected valuation will wait and purchase the good at the regular price only in the event where their realized valuation is high. We characterize the profitmaximizing pricing strategy of the monopolist. Furthermore, adopting a mechanism design perspective, we provide a necessary and sufficient condition under which advance-purchase discounts implement the monopolist’s optimal mechanism.

We analyze relative performance of stochastic and deterministic mechanisms in an environment that has been extensively studied in the literature on communication (e.g., [Vincent P. Crawford, Joel Sobel, Strategic information transmission, Econometrica 50 (6) (1982) 1431–1451]) and optimal delegation (e.g., [Bengt Holmstrom, On the theory of delegation, in: M. Boyer, R.E. Kihlstrom (Eds.), Bayesian Models in Economic Theory, North-Holland, 1984, pp. 115–141]): a principal-agent model with hidden information, no monetary transfers, and single-peaked preferences. We demonstrate that under the common assumption of quadratic payoffs and a certain regularity condition on the distribution of private information and the agent's bias, the optimal mechanism is deterministic. We also provide an explicit characterization of this mechanism.

This paper studies revenue-maximizing auctions when buyers' outside options depend on their private information and are endogenously chosen by the seller. We show that the revenue-maximizing assignment of the object can depend crucially on the outside options that the seller can choose as threats. Depending on the shape of outside options, sometimes an optimal mechanism allocates the object in an ex-post efficient way, and, other times, buyers obtain the object more often than is efficient.

Subsidy-free VCG mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of budget surplus to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss L ˆ ( n , p ) satisfies L ˆ ( n , p ) ⩽ L ˆ ( n , ⌊ n 2 ⌋ ) ⩽ 4 3 n . If p n is bounded away from 1 2 , L ˆ ( n , p ) converges to zero exponentially in n. Participation is voluntary in the optimal mechanism achieving L ˆ ( n , p ) if p = 1 , but not if p ⩾ 2 . Among voluntary mechanisms, the optimal efficiency loss is not significantly larger than L ˆ ( n , p ) if p n ⩽ 1 2 . But it does not converge to zero in n if p n > 1 2 .

Multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price–bundle pair of his choice. We identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules. We then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n -object case. We use these results to characterize environments, mainly distributions of valuations, where bundling is the optimal mechanism in the two and three good cases.

Emerging economies are often exposed to sudden shortages of international financial resources. Yet domestic agents do not seem to take preventive measures against these sudden stops. We highlight the central role played by the limited development of ex ante (insurance) and ex post (spot) domestic financial markets in generating this collective undervaluation of international resources. We study several policies to counteract the external underinsurance. We do this by solving for the optimal mechanism given the constraints imposed by limited financial development, and then considering the main financial policies—in terms of the model and practical relevance—that implement this solution.

This paper finds an optimal mechanism for selling a good to a buyer who may be budget-constrained. We consider a seller with one unit of a good facing a buyer with a quasilinear utility function. If the buyer does not face a binding budget constraint, textbook monopoly pricing is optimal. By contrast, the possibility of a binding budget constraint can make it optimal for the seller to use nonlinear pricing, to commit to a declining price sequence, to require the buyer to disclose his budget, or to offer financing. Journal of Economic Literature Classification Numbers: C70, D42, D45, D89, L12.

In modelling competition among mechanism designers, it is necessary to specify the set of feasible mechanisms. These specifications are often borrowed from the optimal mechanism design literature and exclude mechanisms that are natural in a competitive environment, for example, mechanisms that depend on the mechanisms chosen by competitors. This paper constructs a set of mechanisms that is universal in that any specific model of the feasible set can be embedded in it. An equilibrium for a specific model is robust if and only if it is an equilibrium also for the universal set of mechanisms. A key to the construction is a language for describing mechanisms that is not tied to any preconceived notions of the nature of competition. Journal of Economic Literature Classification Numbers: D43, D89, C72.

It is shown with an example that, in bilateral trade problems with two-sided incomplete information, some seller types may obtain higher expected payos in mechanisms other than the one where they make a take-it-or-leave-it oer, contrary to popular belief. If one looks at the mechanism selection problem of the (informed) seller, then the op- timality of a take-it-or-leave-it oer for the seller is restored. Journal of Economic Literature Classi…cation Numbers: C72, C78, D82.