Gabriel D. Carroll

When Are Local Incentive Constraints Sufficient

We study the question of whether local incentive constraints are sufficient to imply full incentive compatibility in a variety of mechanism design settings, allowing for probabilistic mechanisms. We give a unified approach that covers both continuous and discrete type spaces. On many common preference domains—including any convex domain of cardinal or ordinal preferences, single-peaked ordinal preferences, and successive single-crossing ordinal preferences—local incentive compatibility (suitably defined) implies full incentive compatibility. On domains of cardinal preferences that satisfy a strong nonconvexity condition, local incentive compatibility is not sufficient. Our sufficiency results hold for dominant-strategy and Bayesian Nash solution concepts, and allow for some interdependence in preferences.

An efficiency theorem for incompletely known preferences

There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent is utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions ui[set membership, variant]Ui for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.

Robustness and Separation in Multidimensional Screening

A principal wishes to screen an agent along several dimensions of private information simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principals problem, in which she knows the marginal distribution of each component of the agents type, but does not know the joint distribution. Any mechanism is evaluated by its worst‐case expected profit, over all joint distributions consistent with the known marginals. We show that the optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single crossing) on the structure of preferences within each component. The proof technique involves a generalization of the concept of virtual values to arbitrary screening problems. Sample applications include monopoly pricing and a stylized dynamic taxation model.

Robust contracting with additive noise

We investigate the idea that linear contracts are reliable because they give the same incentives for effort at every point along the contract. We ask whether this reliability leads to a microfoundation for linear contracts, when the principal is profit-maximizing. We consider a principal-agent model with risk neutrality and limited liability, in which the agent observes the realization of a mean-zero shock to output before choosing how much effort to exert. We show that such a model can indeed provide a foundation for reliable contracts, and illustrate what elements are required. In particular, we must assume that the principal knows a lower bound, but not an upper bound, on the shocks.

Informationally robust trade and limits to contagion

Two agents can each accept or reject a proposed deal, whose value for each agent depends on an unknown state, and may be positive or negative. The deal takes place only if both accept. Each agent can be imperfectly informed, in an arbitrary way, about both her own value and the other agents. In such environments, contagious adverse selection may prevent the deal from being reached even when it is mutually beneficial ex post. We give an upper bound on the ex-ante expected welfare loss in equilibrium due to such contagion, valid for any information structure. The welfare loss is small if negative values are unlikely ex ante; and under an assumption of known aggregate gains from the deal, our bound is sharp. The bound has a succinct description, even though the equilibrium itself, in any given information structure, may be hard to describe explicitly.

Robust incentives for effort

We discuss a new perspective on the classic principal-agent problem, which asks how to optimally incentivize an agent to exert costly effort on some task, by rewarding him based on his performance. We review recent results on a robust version of the problem, in which the principal is uncertain about what actions the agent can and cannot take and evaluates an incentive contract based on the worst case over possible environments; the worst-case-optimal contracts turn out to take a simple form.

On the Valuation of Venture Capital Securities

Venture capitalists typically receive preferred stock when they invest. This preferred stock comes in many flavors and can include many different features. The resulting securities can be modeled as a portfolio of options with unknown expiration dates, with these expiration dates possibly correlated to underlying firm value. These securities can provide a significant premium to plain common stock, but past solutions for this premium are either unwieldy or require unrealistic assumptions. In this paper, we derive closed-form solutions for the value of VC securities using a flexible functional form that allows for a wide variety of realistic assumptions for the key parameter values. We then take this solution to the data and estimate the expected premium above common stock for typical VC securities. We find that this premium can be substantial, with estimates between 20 percent and 60 percent for the most common types of transactions.