Contract theory

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In economics, contract theory studies how economic actors can and do construct contractual arrangements, generally in the presence of information asymmetry. Because of its connections with both agency and incentives, contract theory is often categorized within a field known as Law and economics. One prominent application of it is the design of optimal schemes of managerial compensation. In the field of economics, the first formal treatment of this topic was given by Kenneth Arrow in the 1960s. In 2016, Oliver Hart and Bengt R. Holmström both received the Nobel Memorial Prize in Economic Sciences for their work on contract theory, covering many topics from CEO pay to privatizations. Holmström (MIT) focused more on the connection between incentives and risk, while Hart (Harvard) on the unpredictability of the future that creates holes in contracts. [1]


A standard practice in the microeconomics of contract theory is to represent the behaviour of a decision maker under certain numerical utility structures, and then apply an optimization algorithm to identify optimal decisions. Such a procedure has been used in the contract theory framework to several typical situations, labeled moral hazard , adverse selection and signalling . The spirit of these models lies in finding theoretical ways to motivate agents to take appropriate actions, even under an insurance contract. The main results achieved through this family of models involve: mathematical properties of the utility structure of the principal and the agent, relaxation of assumptions, and variations of the time structure of the contract relationship, among others. It is customary to model people as maximizers of some von Neumann–Morgenstern utility functions, as stated by expected utility theory.

Main models of agency problems

Moral hazard

The moral hazard problem refers to the extent to which an employee's behaviour is concealed from the employer: whether they work, how hard they work and how carefully they do so. [2]

In moral hazard models, the information asymmetry is the principal's inability to observe and/or verify the agent's action. Performance-based contracts that depend on observable and verifiable output can often be employed to create incentives for the agent to act in the principal's interest. When agents are risk-averse, however, such contracts are generally only second-best because incentivization precludes full insurance.

The typical moral hazard model is formulated as follows. The principal solves:

subject to the agent's "individual rationality (IR)" constraint,

and the agent's "incentive compatibility (IC)" constraint,


where is the wage for the agent as a function of output , which in turn is a function of effort:.

represents the cost of effort, and reservation utility is given by .

is the "utility function", which is concave for the risk-averse agent, is convex for the risk-prone agent, and is linear for the risk-neutral agent.

If the agent is risk-neutral and there are no bounds on transfer payments, the fact that the agent's effort is unobservable (i.e., it is a "hidden action") does not pose a problem. In this case, the same outcome can be achieved that would be attained with verifiable effort: The agent chooses the so-called "first-best" effort level that maximizes the expected total surplus of the two parties. Specifically, the principal can give the realized output to the agent, but let the agent make a fixed up-front payment. The agent is then a "residual claimant" and will maximize the expected total surplus minus the fixed payment. Hence, the first-best effort level maximizes the agent's payoff, and the fixed payment can be chosen such that in equilibrium the agent's expected payoff equals his or her reservation utility (which is what the agent would get if no contract was written). Yet, if the agent is risk-averse, there is a trade-off between incentives and insurance. Moreover, if the agent is risk-neutral but wealth-constrained, the agent cannot make the fixed up-front payment to the principal, so the principal must leave a "limited liability rent" to the agent (i.e., the agent earns more than his or her reservation utility).

The moral hazard model with risk aversion was pioneered by Steven Shavell, Sanford J. Grossman, Oliver D. Hart, and others in the 1970s and 1980s. [3] [4] It has been extended to the case of repeated moral hazard by William P. Rogerson and to the case of multiple tasks by Bengt Holmström and Paul Milgrom. [5] [6] The moral hazard model with risk-neutral but wealth-constrained agents has also been extended to settings with repeated interaction and multiple tasks. [7] While it is difficult to test models with hidden action empirically (since there is no field data on unobservable variables), the premise of contract theory that incentives matter has been successfully tested in the field. [8] Moreover, contract-theoretic models with hidden actions have been directly tested in laboratory experiments. [9]

Example of possible solution to moral hazard

A study on the solution to moral hazard concludes that adding moral sensitivity to the principal-agent model increases its descriptiveness, prescriptiveness, and pedagogical usefulness because it induces employees to work at the appropriate effort for which they receive a wage. The theory suggests that as employee work efforts increase, so proportional premium wage should increases also to encourage productivity. [10]

Adverse selection

In adverse selection models, the principal is not informed about a certain characteristic of the agent at the time the contract is written. The characteristic is called the agent's "type". For example, health insurance is more likely to be purchased by people who are more likely to get sick. In this case, the agent's type is his or her health status, which is privately known by the agent. Another prominent example is public procurement contracting: The government agency (the principal) does not know the private firm's cost. In this case, the private firm is the agent and the agent's type is the cost level. [11]

In adverse selection models, there is typically too little trade (i.e., there is a so-called "downward distortion" of the trade level compared to a "first-best" benchmark situation with complete information), except when the agent is of the best possible type (which is known as the "no distortion at the top" property). The principal offers a menu of contracts to the agent; the menu is called "incentive-compatible" if the agent picks the contract that was designed for his or her type. In order to make the agent reveal the true type, the principal has to leave an information rent to the agent (i.e., the agent earns more than his or her reservation utility, which is what the agent would get if no contract was written). Adverse selection theory has been pioneered by Roger Myerson, Eric Maskin, and others in the 1980s. [12] [13] More recently, adverse selection theory has been tested in laboratory experiments and in the field. [14] [15]

Adverse selection theory has been expanded in several directions, e.g. by endogenizing the information structure (so the agent can decide whether or not to gather private information) and by taking into consideration social preferences and bounded rationality. [16] [17] [18]


In signalling models, one party chooses how and whether or not to present information about itself to another party to reduce the information asymmetry between them. [19] In signaling models, the signaling party agent and the receiving party principal have access to different information. The challenge for the receiving party is to decipher the credibility of the signaling party so as to assess their capabilities. The formulation of this theory began in 1973 by Michael Spence through his job-market signaling model. In his model, job applicants are tasked with signalling their skills and capabilities to employers to reduce the probabilities for the employer to choose a lesser qualified applicant over a qualified applicant. This is because potential employers lack the knowledge to discern the skills and capabilities of potential employees. [20]

Incomplete contracts

Contract theory also utilizes the notion of a complete contract, which is thought of as a contract that specifies the legal consequences of every possible state of the world. More recent developments known as the theory of incomplete contracts, pioneered by Oliver Hart and his coauthors, study the incentive effects of parties' inability to write complete contingent contracts. In fact, it may be the case that the parties to a transaction are unable to write a complete contract at the contract stage because it is either difficult to reach an agreement to get it done or it is too expensive to do so, [2] e.g. concerning relationship-specific investments. A leading application of the incomplete contracting paradigm is the Grossman-Hart-Moore property rights approach to the theory of the firm (see Hart, 1995).

Because it would be impossibly complex and costly for the parties to an agreement to make their contract complete, [21] the law provides default rules which fill in the gaps in the actual agreement of the parties.

During the last 20 years, much effort has gone into the analysis of dynamic contracts. Important early contributors to this literature include, among others, Edward J. Green, Stephen Spear, and Sanjay Srivastava.

Expected utility theory

Much of contract theory can be explained through expected utility theory. This theory indicates that individuals will measure their choices based on the risks and benefits associated with a decision. A study analyzed that agents' anticipatory feelings are affected by uncertainty. Hence why principals need to form contracts with agents in the presence of information asymmetry to more clearly understand each party's motives and benefits. [22]

Examples of contract theory

Incentive Design

In the contract theory, the goal is to motivate employees by giving them rewards. Trading on service level/quality, results, performance or goals. It can be seen that reward determines whether the incentive mechanism can fully motivate employees. [23]

In view of the large number of contract theoretical models, the design of compensation under different contract conditions is different. [23]

Rewards on Absolute Performance and Relative Performance [23]

Absolute performance-related reward is an incentive mechanism widely recognized in economics in the real society, because it provides employees with the basic option of necessary and effective incentives. But, absolute performance-related rewards have two drawbacks.

  1. There will be people who cheat
  2. Vulnerable to recessions or sudden growth

Design contracts for multiple employees [23]

Considering absolute performance-related compensation is a popular way for employers to design contracts for more than one employee at a time, and one of the most widely accepted methods in practical economics.

There are also other forms of absolute rewards linked to employees' performance. For example, dividing employees into groups and rewarding the whole group based on the overall performance of each group. But one drawback of this method is that some people will fish in troubled waters while others are working hard, so that they will be rewarded together with the rest of the group. It is better to set the reward mechanism as the competitive competition, and obtain higher rewards through better performance.

See also

Related Research Articles

This aims to be a complete article list of economics topics:

Moral hazard Increases in the exposure to risk when insured, or when another bears the cost

In economics, moral hazard occurs when an entity has an incentive to increase its exposure to risk because it does not bear the full costs of that risk. For example, when a corporation is insured, it may take on higher risk knowing that its insurance will pay the associated costs. A moral hazard may occur where the actions of the risk-taking party change to the detriment of the cost-bearing party after a financial transaction has taken place.

A complete contract is an important concept from contract theory.

Adverse selection Selective trading based on possession of hidden information

In economics, insurance, and risk management, adverse selection is a market situation where buyers and sellers have different information. The result is that participants with key information might participate selectively in trades at the expense of other parties who do not have the same information.

Information asymmetry Concept in contract theory and economics

In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. This asymmetry creates an imbalance of power in transactions, which can sometimes cause the transactions to be inefficient causing market failure in the worst case. Examples of this problem are adverse selection, moral hazard, and monopolies of knowledge.

Incentive Something that motivates individuals to perform

An incentive is something that motivates or drives one to do something or behave in a certain way. There are two types of incentives that affect human decision making. These are: intrinsic and extrinsic incentives. Intrinsic incentives are those that motivate a person to do something out of their own self interest or desires, without any outside pressure or promised reward. However, extrinsic incentives are motivated by rewards such as an increase in pay for achieving a certain result; or avoiding punishments such as disciplinary action or criticism as a result of not doing something. 

Experimental economics is the application of experimental methods to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law.

Mechanism design

Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory. It has broad applications, from economics and politics in such fields as market design, auction theory and social choice theory to networked-systems.

Principal–agent problem Conflict of interest when one agent makes decisions on anothers behalf

The principal–agent problem, in political science, supply chain management and economics occurs when one person or entity, is able to make decisions and/or take actions on behalf of, or that impact, another person or entity: the "principal". This dilemma exists in circumstances where agents are motivated to act in their own best interests, which are contrary to those of their principals, and is an example of moral hazard. Issues also arise when companies have an incentive to become increasingly deferential to management that have ownership stakes. As shareholders are dis-incentived to intervene, there are fewer checks on management. Issues can also arise among different types of management.

The term efficiency wages was introduced by Alfred Marshall to denote the wage per efficiency unit of labor. Marshallian efficiency wages would make employers pay different wages to workers who are of different efficiencies such that the employer would be indifferent between more-efficient workers and less-efficient workers. The modern use of the term is quite different and refers to the idea that higher wages may increase the efficiency of the workers by various channels, making it worthwhile for the employers to offer wages that exceed a market-clearing level. Optimal efficiency wage is achieved when the marginal cost of an increase in wages is equal to the marginal benefit of improved productivity to an employer.

The theory of the firm consists of a number of economic theories that explain and predict the nature of the firm, company, or corporation, including its existence, behaviour, structure, and relationship to the market.

Information economics or the economics of information is a branch of microeconomic theory that studies how information and information systems affect an economy and economic decisions. Information has special characteristics: It is easy to create but hard to trust. It is easy to spread but hard to control. It influences many decisions. These special characteristics complicate many standard economic theories.

Personnel economics has been defined as "the application of economic and mathematical approaches and econometric and statistical methods to traditional questions in human resources management". It is an area of applied micro labor economics, but there are a few key distinctions. One distinction, not always clearcut, is that studies in personnel economics deal with the personnel management within firms, and thus internal labor markets, while those in labor economics deal with labor markets as such, whether external or internal. In addition, personnel economics deals with issues related to both managerial-supervisory and non-supervisory workers.

An agency cost is an economic concept that refers to the costs associated with the relationship between a "principal", and an "agent". The agent is given powers to make decisions on behalf of the principal. However, the two parties may have different incentives and the agent generally has more information. The principal cannot directly ensure that its agent is always acting in its best interests. This potential divergence in interests is what gives rise to agency costs.

In contract theory, signalling is the idea that one party credibly conveys some information about itself to another party. Although signalling theory was initially developed by Michael Spence based on observed knowledge gaps between organisations and prospective employees, its intuitive nature led it to be adapted to many other domains, such as Human Resource Management, business, and financial markets.

Motivation crowding theory is the theory from psychology and microeconomics suggesting that providing extrinsic incentives for certain kinds of behavior—such as promising monetary rewards for accomplishing some task—can sometimes undermine intrinsic motivation for performing that behavior. The result of lowered motivation, in contrast with the predictions of neoclassical economics, can be an overall decrease in the total performance.

Screening in economics refers to a strategy of combating adverse selection – one of the potential decision-making complications in cases of asymmetric information – by the agent(s) with less information.

Georges Dionne (professor)

Georges Dionne is a full Professor of Finance who holds the Canada Research Chair in Risk Management at HEC Montréal. He has been a Visiting Scholar in the Department of Risk Management and Insurance at Georgia State University and in the Economics Department at Ecole Polytechnique in France for many years.

The multiple principal problem, also known as the common agency problem, the multiple accountabilities problem, or the problem of serving two masters, is an extension of the principal-agent problem that explains problems that can occur when one person or entity acts on behalf of multiple other persons or entities. Specifically, the multiple principal problem states that when one person or entity is able to make decisions and / or take actions on behalf of, or that impact, multiple other entities: the "principals", the existence of asymmetric information and self-interest and moral hazard among the parties can cause the agent's behavior to differ substantially from what is in the joint principals' interest, bringing large inefficiencies. The multiple principal problem has been used to explain inefficiency in many types of cooperation, particularly in the public sector, including in parliaments, ministries, agencies, inter-municipal cooperation, and public-private partnerships, although the multiple principal problem also occurs in firms with multiple shareholders.


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