Optimal scrutiny in multi-period promotion tournaments

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their skills, and intends to promote one of them at the end. In each period the agents choose effort levels that influence their outputs, and are fully informed of the past history of outputs. The principal's major objective is to maximize the expected total output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and promotes the agent who produces more on the sample. This determines an extensive form game Γ(T,n), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n. More precisely, if η(T) is the maximal optimal sample size, then η(T)/T→0 as T→∞.     

Wealth effects and agency costs

We analyze how the agent's initial wealth affects the principal's expected profits in the standard principal–agent model with moral hazard.We show that if the principal prefers a poorer agent for all specifications of action sets, probability distributions, and disutility of effort, then the agent's utility of income must exhibit a coefficient of absolute prudence less than three times the coefficient of absolute risk aversion for all levels of income, thus strengthening the sufficiency result of Thiele and Wambach (1999). Also, we prove that there is no condition on the agent's utility of income alone that will make the principal prefer richer agents. Moreover, we show that, for an interesting class of problems, the principal prefers a relatively poorer agent if agent's wealth is sufficiently large. Finally, we discuss how alternative ways of modeling the agent's outside option affects the principal's preferences for agent's wealth.     

Pareto-optimal Nash equilibria are competitive in a repeated economy

Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in the time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.     

A Note on Efficiency Wage Theory and Principal–Agent Theory

Why are principal–agent models used in some circumstances and efficiency wage models in others? In this note, it is argued that efficiency wages provide incentives based on an evaluation of the agent's input, while the incentives analysed in principal–agent models rely on the agent's output. The choice between the two incentive schemes depends on the probability that the agent is caught shirking. Moreover, we demonstrate that a combination of input‐ and output‐related elements provides stronger incentives than payment schemes based on merely one of these elements. However, the combination requires a more complex labour contract involving an increased cost of writing the contract. The interaction between this transaction cost and a hiring cost is analysed.     

Mechanism design with collusive supervision

We analyze an adverse selection environment with third party supervision. The supervisor is partly informed of the agent's type. The supervisor and the agent collude while interacting with the principal. Contracting with the agent directly and ignoring the presence of the supervisor constitutes the no-supervision benchmark. We show that delegating to the supervisor reduces the principal's payoff compared to the no-supervision benchmark under a standard condition on the distribution of the agent's types. In contrast, if the principal contracts with both the agent and the supervisor, there exists a mechanism that improves the principal's payoff over the no-supervision payoff.     

Subjective Performance Evaluations and Reciprocity in Principal–Agent Relations

We conduct a laboratory experiment with agents working on, and principals benefiting from, a real effort task in which the agents' performance can only be evaluated subjectively. Principals give subjective performance feedback to agents, and agents have an opportunity to sanction principals. In contrast to existing models of reciprocity, we find that agents tend to sanction whenever the feedback of principals is below their subjective self‐evaluations even if agents' pay‐offs are independent of it. In turn, principals provide more positive feedback (relative to their actual performance assessment of the agent) if this does not affect their pay‐off.     

Minimum payments and induced effort in moral hazard problems

Consider a moral hazard problem in which there is a constraint to pay the agent no less than some amount m. This paper studies the effect of changes in m on the effort that the principal chooses to induce from the agent. We present sufficient conditions on the informativeness of the signal observed by the principal and on the agentʼs utility under which when m increases, induced effort (and hence productivity) falls. We also study how the cost minimizing contract for any given effort level varies in m. We present an efficient algorithm for numerically calculating optimal contracts for given parameters and show that induced effort falls when m is increased in many cases even when our sufficient conditions fail.     

Trading with a common agent under complete information: A characterization of Nash equilibria

We analyze an abstract model of trading where N principals submit quantity-payment schedules that describe the contracts they offer to an agent, and the agent then chooses how much to trade with every principal. This represents a special class of common agency games with complete information. We study all the subgame perfect Nash equilibria of these games, not only truthful ones, providing a complete characterization of equilibrium payoffs. In particular, we show that the equilibrium that is Pareto-dominant for the principals is not truthful when there are more than two of them. We also provide a partial characterization of equilibrium strategies.     

Optimal non-linear income taxation for reduction of envy

This paper examines the optimal non-linear income taxation problem based on λ-equitability. An allocation is λ-equitable if no agent envies a proportion λ of the bundle of any other agent. We examine the properties of Pareto undominated allocations for various λ-equitability requirements. When there is one output, the marginal income tax rate can increase only if leisure is a luxury. In a multi-commodity model with commodity taxes, the goods preferred by the low skilled agent and/or those with high Hicksian elasticities are taxed more heavily. When preferences exhibit quasi-linearity, we can show that the introduction of the λ-equitability constraint increases the marginal income tax rates of the entire population.     

SUBJECTIVE EVALUATION IN AGENCY CONTRACTS*

We study how a principal uses her subjective evaluation of the agent's performance in an incentive contract. It is shown that the subjective evaluation can be used either 1) when there is no other information about the agent's performance and the principal is able to discard money, or 2) when the principal chooses between wage payment based on subjective evaluation by foregoing objective evaluation, and the one based only on the objective evaluation and when the subjective evaluation is sufficiently accurate. The principal pays a high fixed wage when her rating at the subjective evaluation is above a certain level. On the other hand, when it is below that level, she either pays a low fixed wage or obtains objective evaluation and pays based on its outcome.     

Credible delegation

We show that the vertical delegation of decision-making authority to agent firms can act as a credible strategic commitment even when contracts are unobservable (or renegotiable) if and only if multilateral delegation is combined with decentralized ownership of the agent firms. In this case, the possibility of renegotiation of other agents’ contracts constrains the set of contracts acceptable to each agent. Delegation may induce more or less aggressive behavior, depending on the nature of within-structure competition among the agent firms. Thus, delegation may be a valuable, credible strategic commitment mechanism when strategies are either substitutes or complements.     

Perfect communication equilibria in repeated games with imperfect monitoring

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

A note on capital markets and bankruptcy constraints in contracting

This note considers the extent to which state-contingent bankruptcy constraints in a standard contracting problem with adverse selection can be mitigated by a risk-neutral third party. It shows that if payoffs of principal and agent are quasi-linear, the third party can only affect the constraints if it has complete information about the agent's type — observing a correlated signal is not enough.     

Moral hazard with bounded payments

We study the moral hazard problem with general upper and lower constraints M on compensation. We characterize the optimal contract and show existence and uniqueness. When minimizing costs for given effort, a principal harmed by M will pay according to M on some range of outcomes; when M reflects limited liability or a minimum wage, the contract is option-like. When the principal also chooses effort, a principal harmed by M might nonetheless never pay according to M. This cannot occur if the cost of inducing effort in the standard principal-agent problem is convex, for which we provide sufficient conditions related to the informativeness of outcome about effort.     

Time Horizon and the Discount Rate

We consider an economy à la Lucas (1978, Econometrica46 , 1429-1446) with a risk-averse representative agent. The exogenous growth rate of the economy follows a random walk. We characterize the set of utility functions for which it is efficient to discount more distant cash flows at a lower rate. The benchmark result is that, when the growth rate is almost surely nonnegative, the yield curve is decreasing if and only if relative risk aversion is decreasing with wealth. Relaxing the assumption on the absence of recession requires more restrictions on preferences, such as increasing relative prudence. Journal of Economic Literature Classification Numbers: D81, D91, Q25, Q28.     

The nature of tournaments

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen in J Polit Econ 89:841?C864, 1981). We find that it is often optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (1) R is small relative to P (where R is risk aversion and P is absolute prudence); (2) the distribution of shocks to output is asymmetric and the asymmetry takes a particular form; (3) the principal faces a limited liability constraint; and (4) there is agent heterogeneity of a particular form.     

Economic evaluations in migraine: systematic literature review and a novel approach

Abstract

Background: For novel migraine therapies, economic evaluations will be required to understand the trade-offs between additional health benefit and additional cost. The purpose of this study was to conduct a systematic literature review (SLR) to identify previous economic evaluations in migraine from the United Kingdom or Irish perspective to critically appraise these evaluations and to propose, if necessary, a novel modelling approach that can be used for future economic evaluations of migraine therapies.

Methods: An SLR was conducted to identify previous economic evaluations of preventive migraine treatments. Key opinion leaders were consulted to determine the criteria for a robust migraine economic evaluation. Economic evaluations identified in the SLR were appraised against these criteria, and a novel cost-effectiveness model structure was then proposed.

Results: Eight records reporting on published economic evaluations were identified and critically appraised for general quality. Expert consultation provided 6 recommendations on the ideal model structure for migraine that is both clinically and economically meaningful. A decision-tree plus Markov structure was then developed as a cost-effectiveness model for migraine therapies where each health state is associated with a patient distribution across monthly migraine day (MMD) frequencies.

Conclusions: Future migraine economic evaluations should allow for assessments across the full spectrum of migraine, a response-based stopping rule, and the estimation of benefits and resource costs based on MMD frequency. The approach proposed in this paper captures all of the desired elements for an economic evaluation of migraine therapy and is suitable to assess new migraine therapies.     

A theory of subjective compound lotteries

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.     

The principal-agent problem with a satisficing agent

The principal-agent problem is formulated with an expected utility maximizing principal and a satisficing agent. If the outcome set is finite and if there is only one aspiration level, then there are always optimal incentive schemes which can be represented by vectors having only the unique aspiration level and zero as coordinate values. The relation between the monotone likelihood ratio property and the monotonicity of optimal incentive schemes is investigated. This is done not only in the above model, but also in a continuous model with outcomes in an interval, which is much more interesting.