Erratum to “Negotiation and take it or leave it in common agency”: [Journal of Economic Theory 111 (2003) 88-109]

The no-externalities condition provided in the text is not sufficient for Theorems 3 and 4 when effort is not fully contractable. In the case where the principals cannot contract at all on agent's effort, the condition in the text requires that for any set of alternatives offered by the principal there is one that is at least as good as all other alternatives in the set for the agent no matter what the other principal does, no matter what effort the agent takes, and no matter what the agent's type. In fact, a stronger condition is required. For any set of alternatives offered by a principal, each of the choices within this set that is at least as good for the agent as any other choice within the set must remain so no matter what actions the other principals take, no matter what effort the agent takes, and no matter what the agent's type.     

Dynamic contracting with persistent shocks

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound—immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.     

Ranking of information systems in agency models: an integral condition

Summary. We provide a condition for ranking of information systems in agency problems. The condition has a straightforward economic interpretation in terms of the sensitivity of a cumulative distribution with respect to the agent's effort. The criterion is shown to be equivalent to the mean preserving spread condition on the likelihood ratio distributions. Received: November 10, 1999; revised version: February 17, 2000     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

Moral Hazard and Bargaining Power

Abstract. We introduce bargaining power in a moral hazard framework where parties are risk-neutral and the agent is financially constrained. We show that the same contract emerges if the concept of bargaining power is analyzed in either of the following three frameworks: in a standard principal–agent (P–A) framework by varying the agent's outside opportunity, in an alternating offer game, and in a generalized Nash-bargaining game. However, for sufficiently low levels of the agent's bargaining power, increasing it marginally does affect the equilibrium in the Nash-bargaining game, but not in the P–A model and in the alternating offer game.     

Wealth Effects, Incentives, and Productivity

Comparative static effects of varying the wealth level of a risk-averse agent in a moral hazard setting with limited liability constraints are investigated. There are two principal opposing effects of increasing wealth: the incentive effect, which allows stronger punishments for poor performance, thereby encouraging higher effort; and the preference effect, which reduces the agent's effort incentives owing to income effects in the demand for leisure. It is shown that optimal effort levels are initially constant, subsequently increasing and eventually decreasing in wealth. Hence agents with intermediate wealth levels are the most productive.     

Optimal risk-sharing with effort and project choice

We consider first-best risk-sharing problems in which “the agent” can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the functional form of the option is obtained as a solution to an ordinary differential equation. In the general case, the optimal contract is a fixed point of a functional that connects the agent's and the principal's maximization problems. We apply martingale/duality methods familiar from optimal consumption-investment problems.     

Correlated information, mechanism design and informational rents

Crémer and McLean (Econometrica 56 (1988) 1247-1258) obtain a sufficient and necessary condition for full surplus extraction in Bayesian-Nash equilibrium—the rank condition, which McAfee and Reny (Econometrica 60(2) (1992) 395-421) later generalize for continuous type spaces. This paper shows that, if the principal does not know how noisy is the agent's signal—or equivalently, when signals available to an agent can be ranked by Blackwell's informativeness and, an agent's informativeness is independent of others’ information, the rank condition fails to hold. Conversely, when rank condition fails and informational rents are left to an agent, the model can be interpreted as if, the principal were uncertain about the informativeness of the agent's signal.     

A Continuous-Time Version of the Principal–Agent Problem

This paper describes a new continuous-time principal–agent model, in which the output is a diffusion process with drift determined by the agent's unobserved effort. The risk-averse agent receives consumption continuously. The optimal contract, based on the agent's continuation value as a state variable, is computed by a new method using a differential equation. During employment, the output path stochastically drives the agent's continuation value until it reaches a point that triggers retirement, quitting, replacement, or promotion. The paper explores how the dynamics of the agent's wages and effort, as well as the optimal mix of short-term and long-term incentives, depend on the contractual environment.     

Adverse selection problems without the Spence-Mirrlees condition

This paper studies a class of one-dimensional screening problems where the agent's utility function does not satisfy the Spence-Mirrlees condition (SMC). The strength of the SMC for hidden information problems is to provide a full characterization of implementable contracts using only the local incentive compatibility (IC) constraints. These constraints are equivalent to the monotonicity of the decision variable with respect to the agent's unobservable one-dimensional parameter. When the SMC is violated the local IC constraints are no longer sufficient for implementability and additional (global) IC constraints have to be taken into account. In particular, implementable decisions may not be monotonic and discretely pooled types must have the same marginal utility of the decision (or equivalently, get the same marginal tariff). Moreover, at the optimal decision, the principal must preserve the same trade-off between rent extraction and allocative distortion measured in the agent's marginal rent unit. In a specific setting where non-monotone contracts may be optimal we fully characterize the solution.     

Wealth Effects, Distribution, and the Theory of Organization

We construct a general equilibrium model of firm formation in which organization is endogenous. Firms are coalitions of agents providing effort and investment capital. Effort is unobservable unless a fixed monitoring cost is paid, and borrowing is subject to a costly state verification problem. Because incentives vary with an agent's wealth, different types of agents become attractive firm members under different circumstances. When borrowing is not costly, firms essentially consist of one type of agent and are organized efficiently. But when the costly state verification problem is sufficiently severe, firm organization will depend on the distribution of wealth: with enough inequality, it will tend to be dictated by incentives of rich agents to earn high returns to wealth, even if the chosen organizational form is not a technically efficient way to provide incentives.Journal of Economic LiteratureClassification Numbers: D2, D31, J41, L2.     

Contracting with imperfect commitment and noisy communication

This paper provides new analytical tools for studying principal-agent problems with adverse selection and limited commitment. By allowing the principal to use general communication devices we overcome the literature's common, but overly restrictive focus on one-shot, direct communication. In addition, general communication devices solve two fundamental problems of contracting with imperfect commitment: First, they allow us to identify the ‘local downward’ incentive constraints as the relevant ones if the agent's preferences satisfy a single-crossing property. Second, we show how one may restrict the cardinality of the message spaces of the communication device. An example illustrates our arguments and the suboptimality of one-shot, direct communication.     

Optimal use of correlated information in mechanism design when full surplus extraction may be impossible

We study the mechanism design problem when the principal can condition the agent's transfers on the realization of ex post signals that are correlated with the agent's types. Crémer and McLean [Econometrica 53(1985) 345-361; 56(1988) 1247-1257], McAfee and Reny [Econometrica 60(2)(1992) 395-421], and Riordan and Sappington [J. Econ. Theory, 45(1988) 189-199] studied situations where the signals are such that full surplus can be extracted from every agent type. We study optimal utilization of the signals when there are fewer signals than types and the Riordan and Sappington conditions do not always hold. For some special cases, we show the level of surplus that can be extracted, and identify the agent types who obtain rent.     

Matching with noise and the acceptance curse

This paper explores matching with both search and information frictions. Specifically, everyone observes only a noisy signal of the true type of any potential mate. In this context, matching decisions must incorporate not only information about a partner's attribute conveyed by the noisy signal, but also—as in the winner's curse in auction theory—information about a partner's type contained in his or her acceptance decision.We show that there exists an equilibrium exhibiting a stochastic positive assorting of types, generalizing [Becker, J. Polit. Economy 81 (1973) 813-846]. In equilibrium, selection is adverse: being accepted reduces an agent's estimate of a potential partner's type, a phenomenon that we call the acceptance curse effect.     

Veto-based delegation

In a principal-agent model with hidden information and no monetary transfers, I establish the veto-power principle: the principal can implement an optimal outcome through veto-based delegation with a properly chosen default decision. This result demonstrates the exact nature of commitment powers required by the principal: to design the default outcome and to ensure that she has almost no formal control over the agent's decisions.     

On the bad reputation of reputational concerns

Can reputational concerns do any good? Economists have shown how they lead agents to ignore valuable information, to herd, and to become overly risk averse. We explore how they may be a social blessing. An agent may exert effort to become informed about the uncertain benefits of a project. A smart agent's efforts make him better informed; a dumb agent's efforts are to no avail. If an agent does not know his type, reputational concerns are socially beneficial. If an agent knows his type, reputational concerns may be socially beneficial. A dumb agent takes inefficient, unconventional decisions to mimic a smart agent. The latter exerts more effort in order not to be mistaken for a dumb. This holds whether or not project rejection is a safe haven for the dumb.     

Discretionary rewards as a feedback mechanism

This paper studies the use of discretionary rewards in a finitely repeated principal–agent relationship with moral hazard. The key aspect is that rewards have informational content. When the principal obtains a private subjective signal about the agent's performance, she may pay discretionary bonuses to provide credible feedback to the agent. In accordance with the often observed compression of ratings, we show that in equilibrium the principal communicates the agent's interim performance imperfectly, i.e., she does not fully differentiate good and bad performance. Furthermore, we show that small rewards can have a large impact on the agent's effort, provided that the principal's stake in the project is small.     

Selling options

Contracts often take the form of options: oil fields can be abandoned, planning permission may go unused, and acquired firms can be liquidated. We consider a seller who auctions a dynamic option among N agents. After the auction, the economy evolves and the winning bidder chooses both if and when to execute the option. The revenue-maximising auction consists of an up-front bid and a contingent fee, where the latter is chosen in a Pigouvian manner, so the winning agent's choice of exercise time maximises the seller's revenue. This contingent payment is time- and state-invariant, so the seller does not have to observe post-auction information in order to implement the optimal auction. The revenue-maximising mechanism induces a dynamic distortion: the option is exercised later than under the comparable welfare-maximising mechanism.     

Stochastic mechanisms in settings without monetary transfers: The regular case

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 Holmström, 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.     

Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest “approval”. It is efficient, strategyproof, anonymous and neutral.We reach an impossibility if, in addition, each agent's utility is at least , where n is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.