Ex post implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and—in economic environments—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints.We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satisfies Maskin monotonicity.     

On the uniqueness of Groves mechanisms and the payoff equivalence principle

Consider a standard mechanism design setting with quasi-linear preferences and private valuations. From Holmström (1979), we know that if the valuations are smooth with respect to types then any efficient, dominant strategy mechanism is in the class of Groves mechanisms. Here I show that, given regular assumptions on the primitives of the design problem, a weaker condition that includes the case of non-smooth valuations is sufficient and necessary for the uniqueness of Groves mechanisms among all efficient, dominant strategy mechanisms. This condition, which imposes a restriction on the behavior of the one-sided directional derivatives of the valuation functions with respect to individual types, is also shown to be sufficient and necessary to obtain the Payoff Equivalence principle for dominant strategy mechanisms whose choice rules are affine maximizers.     

Bilateral trade with apositional traders

We study the standard model of bilateral trade under incomplete information dropping the assumption that traders know on which side of the market they are. We consider two mechanisms that differ only in the number of offers that an agent can submit. These mechanisms are realistic and they are ex post individually rational (i.e. regret free), while the usual mechanisms proposed in the literature satisfy the weaker requirement of interim individual rationality. Properties of the Bayesian equilibria are described for the general case. For the case where valuations are uniformly distributed in the unit square, two types of equilibria are derived for each mechanism and their efficiency properties are analyzed. As expected, the equilibria under the double offer mechanism are less inefficient than those under the single offer mechanism.     

Robust Implementation in Direct Mechanisms

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages lead to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent-value environment with single-crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that the interdependence is not too high. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one.     

English auctions and the Stolper-Samuelson theorem

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the Stolper-Samuelson theorem, one for economies with n goods and n factors, and one for non-square economies. Similar assumptions and methods underlie these seemingly unrelated results.     

Finite supermodular design with interdependent valuations

This paper studies supermodular mechanism design in environments with arbitrary (finite) type spaces and interdependent valuations. In these environments, the designer may have to use Bayesian equilibrium as a solution concept, because ex-post implementation may not be possible. We propose direct (Bayesian) mechanisms that are robust to certain forms of bounded rationality while controlling for equilibrium multiplicity. In quasi-linear environments with informational and allocative externalities, we show that any Bayesian mechanism that implements a social choice function can be converted into a supermodular mechanism that also implements the original decision rule. The proposed supermodular mechanism can be chosen in a way that minimizes the size of the equilibrium set, and we provide two sets of sufficient conditions to this effect. This is followed by conditions for supermodular implementation in unique equilibrium.     

Optimal pricing and capacity choice for a public service under risk of interruption

We develop rules for pricing and capacity choice for an interruptible service that recognize the interdependence between consumers’ perceptions of system reliability and their market behavior. Consumers post ex ante demands, based on their expectations on aggregate demand. Posted demands are met if ex post supply capacity is sufficient. However, if supply is inadequate all ex ante demands are proportionally interrupted. Consumers’ expectations of aggregate demand are assumed to be rational. Under reasonable values for the consumer’s degrees of relative risk aversion and prudence, demand is decreasing in supply reliability. We derive operational expressions for the optimal pricing rule and the capacity expansion rule. We show that the optimal price under uncertainty consists of the optimal price under certainty plus a markup that positively depends on the degrees of relative risk aversion, relative prudence and system reliability. We also show that any reliability enhancing investment—though lowering the operating surplus of the public utility—is socially desirable as long as it covers the cost of investment.     

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.     

Simple contracts, renegotiation under asymmetric information, and the hold-up problem

In this article it is demonstrated that voluntary bargaining over a collective decision under asymmetric information may well lead to ex post efficiency if the default decision is non-trivial. It is argued that the default decision may be interpreted as a ‘simple’ contract that the parties have written ex ante. This result is used in order to show that simple unconditional contracts which are renegotiated may allow the hold-up problem to be solved, even if the parties’ valuations are private information.     

Optimal combinatorial mechanism design

We consider an optimal mechanism design problem with several heterogenous objects and interdependent values. We characterize ex post incentives using an appropriate monotonicity condition and reformulate the problem in such a way that the choice of an allocation rule can be separated from the choice of the payment rule. Central to the analysis is the formulation of a regularity condition, which gives a recipe for the optimal mechanism. If the problem is regular, then an optimal mechanism can be obtained by solving a combinatorial allocation problem in which objects are allocated in a way to maximize the sum of virtual valuations. We identify conditions that imply regularity using the techniques of supermodular optimization.     

Robust implementation in general mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.     

Status Quo Bias in Bargaining: An Extension of the Myerson-Satterthwaite Theorem with an Application to the Coase Theorem

We generalize the Myerson-Satterthwaite theorem to study inefficiencies in bilateral bargaining over a divisible good, with two-sided private information on the valuations. For concave quasi-linear preferences, the ex ante most efficient Bayes equilibrium of any mechanism always exhibits a bias toward the status quo. If utility functions are quadratic every Bayes equilibrium is ex post inefficient, with the expected amount of trade biased toward the disagreement point. In other words, for the class of preferences we study, there is a strategic advantage to property rights in the Coase bargaining setup in the presence of incomplete information. Journal of Economic Literature Classification Numbers: C78, D23, D62, D82.     

Reallocation of corporate resources and managerial incentives in internal capital markets

Diversified firms often trade at a discount with respect to their focused counterparts. The literature has tried to explain the apparent misallocation of resources with lobbying activities or power struggles. We show that diversification can destroy value even when resources are efficiently allocated ex post. When managers derive utility from the funds under their purview, moving funds across divisions may diminish their incentives. The ex ante reduction in managerial incentives can more than offset the increase in firm value due to the ex post efficient reallocation of funds. This effect is robust to the introduction of monetary incentives. Moreover we show that asymmetries in size and growth prospects increase the diversification discount.     

Ascending price Vickrey auctions for general valuations

Ascending price auctions involving a single price path and buyers paying their final bid price cannot achieve the Vickrey-Clarke-Groves (VCG) outcome in the combinatorial auctions setting. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a class of ascending price auctions in which buyers bid on a single price path. Truthful bidding by buyers is an ex post Nash equilibrium in such auctions. By giving discounts to buyers from the final price, the VCG outcome is achieved for general valuations.     

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.     

MEETINGS AND MECHANISMS

This article shows how meeting frictions affect equilibrium trading mechanisms and allocations in an environment where identical sellers post mechanisms to compete for buyers with ex ante heterogeneous private valuations. Multiple submarkets can emerge, each consisting of all sellers posting a particular mechanism and the buyers who visit those sellers. Under mild conditions, high-valuation buyers are all located in the same submarket, and low valuation buyers can be in: (i) the same submarket, (ii) a different submarket, and (iii) a mixture of (i) and (ii). The decentralized equilibrium is efficient when sellers can post auctions with reserve prices or entry fees.     

Water allocation,crop choice,and priority services

We analyze the problem of allocating irrigation water among heterogeneous farmers when water supply is stochastic. If farmers are risk-neutral, a spot market for water is efficient; while the oft-used uniform rationing system is inefficient, both ex ante and ex post. Indeed, we show that it leads farmers to overexpose to risk, thus making shortages more severe and more frequent in case of drought. We propose instead a regulation by priority classes extending Wilson, and we derive an efficiency result. We characterize the set of farmers that would win or lose from such a reform. We also argue that a system of priority classes may be preferred to a spot market system, because scarcity is easier to manage ex ante than ex post, and because this system facilitates the supply of insurance to risk-averse agents.     

Location decisions of a polluting firm and the time consistency of environmental policy

This paper considers location decisions of a monopolist, who faces a tax on its emissions in the home country, under ex post that is, time consistent, and ex ante, that is precommitment, environmental policies. We show that the monopolist will relocate more often under ex post optimal emission taxes. A government which cannot commit to an ex ante emission tax and sets its tax ex post after abatement effort has been chosen, is unable to affect the monopolist’s location decision, because it cannot commit to strategically reduce its tax level in the first stage. Domestic welfare is often higher under ex post emission taxes whenever the monopolist relocates under both policy regimes. Otherwise, welfare is higher under government commitment to an ex ante emission tax level. Thus, government commitment to a policy is not always welfare improving.     

Increasing consumer well-being: risk as potential driver of happiness

This article investigates the relation between risk and individual well-being. We propose a theoretical model of happiness that makes a distinction between ex ante evaluations of happiness and ex post assessments. The main assumptions of the model are tested through three studies based on anchoring vignettes. We show that, even if, ex ante, consumers fear high risk and do not associate it to a high level of happiness, their ex post evaluation of well-being is generally higher when identical consequences result from a high-risk situation than from a low-risk situation. Control over risk-taking reinforces the gap between ex ante and ex post measures of happiness. Thus, our article provides empirical evidence about a positive relation between risk and individual well-being, suggesting that risky experiences have the potential to increase consumer well-being.     

Ex ante efficiency implies incentive compatibility

We show that when agents become informationally negligible in a large economy with asymmetric information, every ex ante efficient allocation must be incentive compatible. This means that any ex ante core or Walrasian allocation is incentive compatible. The corresponding result is false for fixed finite-agent economies with asymmetric information. An example is also constructed to show that the ex post version of the result does not hold. Furthermore, we show that the result is sharp in the sense that it will fail to hold if one relaxes any of the main assumptions, namely, strong conditional independence on the information structure, strict concavity on the utility functions, type independence on the utility functions and endowments.