Relative performance evaluation in a multi-plant firm

Summary. We analyze optimal compensation schedules for the directors of two plants belonging to the same owner and producing the same good but serving geographically differentiated markets. Since the outcome of each director depends on his own effort and on a random variable representing market conditions, the problem takes the form of a principal multi-agent model. We first provide appropriate extensions of the MLR and CDF conditions that ensure the validity of the first-order approach in the single agent case. Then, we show that affiliation of the random variables is a necessary and sufficient condition for the compensation of one director to negatively and monotonically depend on the performance of the other.Received: 23 July 2004, Revised: 18 February 2005, JEL Classification Numbers: D23, D82.I thank Ray Rees and an anonimous referee for helpuful comments and suggestions. Support from CES (Center for Economic Studies), University of Munich is gratefully aknowledged.     

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the ‘state-space' and ‘parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control.     

Executive compensation: a calibration approach

Summary. We use a version of the Grossman and Hart principal-agent model with 10 actions and 10 states to produce quantitative predictions for executive compensation. Performance incentives derived from the model are compared with the performance incentives of 350 firms chosen from a survey by Michael Jensen and Kevin Murphy. The results suggest both that the model does a reasonable job of explaining the data and that actual incentives are close to the optimal incentives predicted by theory. Received: August 12, 1997; revised version: October 27, 1997     

Risk aversion, moral hazard, and the principal's loss

Summary. In their seminal paper on the principal-agent model with moral hazard, Grossman and Hart (1983) show that if the agent's utility function is , then the loss to the principal from being unable to observe the agent's action is increasing in the agent's degree of absolute risk aversion. Their proof is restricted to the case where the number of observable outcomes is equal to two, and it uses an argument that is specific to that case. In this note, we provide an alternative proof that generalizes their result to any (finite) number of outcomes. Received: March 21, 2001; revised version: June 21, 2001     

Adverse selection under ignorance

Summary. We examine an adverse selection relationship in which the principal may ignore the ex ante distribution of the agent's types. The principal's behavior is described by a disutility function that covers the standard minimax regret and minimax loss criteria. We show that the incentive compatible and individually rational mechanism, which minimizes the maximal (or the minimal) principal's disutility over a set of priors, requires the efficient agents to realize the corresponding first-best actions and may demand actions lower than the first-best ones from less efficient agents. We also analyze the qualitative differences between the case in which the principal considers regrets and the case in which he considers losses. Received: 19 October 1998; revised version: 9 November 1999     

Comparing competition and collusion: a numerical approach

Summary. Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. Received: January 14, 2000; revised version: February 28, 2001     

Preference for flexibility in infinite horizon problems

Summary. We consider the extension of the classical problem of preference for flexibility to many periods. Preferences are defined over sets of infinite paths of choices. The main result provides a set of axioms on preferences that yield an additive representation over a subjective state space. This space is the set of preferences over choice today and feasible set tomorrow. The main new axiom, stochastic dominance, is a stronger form of the assumption of monotonicity. Received: September 11 2000; revised version: December 18, 2001     

Competitive search markets for durable goods

Summary. This paper considers a dynamic version of Akerlof's (1970) lemons problem where buyers and sellers must engage in search to find a trading partner. We show that if goods are durable, the market itself may provide a natural sorting mechanism. In equilibrium, high-quality goods sell at a higher price than low-quality goods but also circulate longer. This accords with the common wisdom that sellers who want to sell fast may have to accept a lower price. We then compare the equilibrium outcomes under private information with those under complete information. Surprisingly, we find that for a large range of parameter values the quilibrium outcomes under the two information regimes coincide, despite the fact that circulation time is used to achieve separation. Received: August 24, 2000; revised version: October 24, 2000     

An experimental study of decisions in dynamic optimization problems

Summary. We study decisions of subjects who are given an incentive to solve dynamic optimization problems with the structure of a single-agent, one-sector, closed economy macroeconomic model. The decision task involves a sequence of choices of consumption and investment levels. Treatment variables consist of the initial endowment of capital stock, the production technology available to the economy, and the method of creating the structure of an infinite-horizon model. The study includes and contrasts data from both American and Japanese participants. We find that whether over- or underinvestment relative to the optimum occurs depends on the production technology, but not on the initial endowment of capital stock, nor the subject pool used, nor the method of implementing the infinite horizon. Sudden episodes of maximal consumption called binges, which are always suboptimal, are widely observed. Received: December 7, 1998; revised version: March 12, 1999     

Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach

Summary. With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, this paper studies a model in which the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise because firms need time to build, that is, cannot adjust capacity instantaneously in the post-entry game. This approach produces a simple and intuitive set of equilibrium behaviors and generates clear predictions about when these different outcomes are likely to arise. Our model also departs substantially from the existing literature in concluding that sunkness of capacity costs is neither necessary nor sufficient for capacity to have precommitment value. Received: August 25, 1999; revised version: October 15, 1999     

Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

Summary. Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when is the commodity space, is weakened to allow applications to continuous-time problems, and especially to peak-load pricing when the users' utility and production functions are Mackey continuous. A general form for production sets with the required property is identified, and examples are given of technologies which meet the weakened but not the original condition: these include industrial use and storage of cyclically priced goods. This gives a framework for settling Boiteux's conjecture on the shifting-peak problem. To make clear the restriction implicit in Mackey continuity, we interpret it as interruptibility of demand; and we point out that, without this assumption, the equilibrium can feature pointed peaks with singular, instantaneous capacity charges. The general equilibrium results are supplemented by results for prices supporting individual consumer or producer optima. Received: February 16, 2000; revised version: July 7, 2001     

Common knowledge and quantification

Summary. The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge predicate logics with finite Hilbert-style axiomatizations, prove their completeness, and single out a number of decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable. Received: March 7, 2001; revised version: April 4, 2001     

A reconsideration of the problem of social cost: Free riders and monopolists

Summary. One version of the Coase Theorem is, If property rights are fully allocated, competition leads to efficient allocations. This version implies that the public goods problem can be solved by allocating property rights fully. We show that this mechanism is not likely to work well in economies with global externalities because the privatized economy is highly susceptible to strategic behavior: The free-rider problem manifests itself as a complementary monopoly problem in an associated private goods economy. Thus, our work relates the validity of the Coase Theorem to the literature on the incentives for strategic behavior in economies with complementarities. Received: 12 May 1999; revised version: 9 July 1999     

Mechanism design in queueing problems

Summary.   A well-known result in incentive theory is that for a very broad class of decision problems, there is no mechanism which achieves truth-telling in dominant strategies, efficiency and budget balancedness (or first best implementability). On the contrary, Mitra and Sen (1998), prove that linear cost queueing problems are first best implementable. This paper is an attempt at identification of cost structures for which queueing problems are first best implementable. The broad conclusion is that, this is a fairly large class. Some of these first best implementable problems can be implemented by mechanisms that satisfy individual rationality. Received: October 19, 1999; revised version: March 13, 2000.     

Convergence for difference equations with vanishing time-dependence, with applications to adaptive learning

Summary. We provide conditions for local stability and instability of an equilibrium point in certain systems of nonautonomous nonstochastic difference equations. In the systems under study the influence of time is present through a positive scalar “gain” parameter which converges in the limit to zero. These systems have recently been used to study the dynamics of adaptive learning in economic models, and we provide two economic illustrations of the formal results. Received: October 7, 1997; revised version: February 8, 1999     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

On the inconsistent behavior in voting for incumbents and for term limitation

This paper considers the seemingly inconsistent behavior of individuals who simultaneously vote for incumbents and for limitations on their terms in office. We argue that such behavior may occur even if voters pursue their self-interests in both candidate and term-limitation elections. First, we formulate elections for Congressional candidates as a two-person game, where each candidate maximizes votes by proposing a distribution of benefits to voters. Then we discuss the term limitation at the state level, where voters in each district compare, over time, the average benefits obtained from two alternative series of campaign games: one with a longer tenure associated with no term limit and the other with a shorter tenure created by the introduction of a term limit. In elections of candidates for Congress, the incumbent is successful because he can generate more aggregate benefits for voters. We show, however, that at some critical point of the tenure, his behavior will be less beneficial to his core constituents. In term-limitation elections, those voters tend to support a term limit. In some cases, they represent a majority in the state, and term limits are enacted. Received: February 23, 1999; revised version: January 24, 2000     

On the efficiency of markets for managers

Summary. This paper examines the efficiency of the outside labor market in inducing optimal managerial behavior in the presence of learning. It shows that the incentives provided by the market can be more efficient than the original analysis of Holmstr?m [6] would suggest. Moreover, under a mild additional assumption, the existence of an -efficient equilibrium can be guaranteed if a manager is patient. This result supports Fama's [4] original idea that the outside labor market can be efficient in disciplining top managers. These results also suggest that the empirically documented low levels of explicit incentives for managers might be due to the presence of implicit incentives provided by the outside market. Received: March 18, 1997; revised version: April 19, 2000     

A new proof of the maximum principle

Summary. We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Received: April 11, 2002; revised version: June 26, 2002 Correspondence to: K. Shimomura