14 Contracts

Chapter 14

Contracts

In the previous chapter we examined the several key concepts related to the bargaining process, including value creation and division, bargaining with symmetric and asymmetric impatience, and the last-mover’s advantage. In many business settings, once negotiations are completed, it is time to prepare a contract.

The contract is a defining characteristic of many business and economic relationships. It is a formal agreement that obligates the parties to perform, or refrain from performing, a specified act in exchange for something of value. Labor contracts summarize negotiations between firms and workers over wages, health benefits, work assignments, and so on. Loan contracts between lenders and borrowers specify interest rates, debt service payments, collateral requirements, and restrictive covenants. Contracts between firms and resource suppliers stipulate input prices, raw materials and components specifications, and delivery schedules. Homeowners sign service contracts with landscapers, building contractors, personal and property security providers, and insurance companies. Nations sign bilateral and multilateral treaties that define tariffs, intellectual property rights, human rights, laws of the sea, environmental regulations, military cooperation, and international security agreements.

Contracts are important because they reduce uncertainty by clearly specifying the obligations of the contracting parties. Contracts are necessary because many business relationships resemble prisoner’s-dilemma-type games—each player benefits from cooperation, but each has an incentive to violate the terms of the agreement. If this were not the case, legally binding written contracts would be replaced with verbal agreement and a handshake.1 A contract can transform an unstable coalition into a Nash equilibrium by changing the payoffs in the event of a breech.

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Explicit and implicit contracts lie at the heart of virtually all market transactions. For this reason, contract law is among the most important areas of jurisprudence. Since contract law is extremely complex, anything approaching a detailed discussion of its intricacies is beyond the scope of this book and the expertise of the author. The purpose of this chapter is to illustrate how game theory can be used to enhance our understanding of elements that are common to all contracts.

CONTRACTING ENvIRONMENT

The contracting environment refers to those factors that directly or indirectly affect interaction between and among the contracting parties. This interaction may be referred to as the parties’ contractual relationship. The contracting environment may include participation of third parties, such as the judges, mediators and arbitrators, in the event of a breach by either party. These third parties may be considered players that have the authority to take actions that can affect the outcome by changing the payoffs.

Contractual relationships can be conceptually divided into two phases. The contracting phase refers to negotiations and other interactions between the parties that come to define the terms of the contract. This is followed by the implementation phase in which the contract is executed and enforced. There are two fundamental ways in which a contract may be enforced. A contract is self-enforced if it is in the players’ individual interest to abide by the terms of the contract. A contract is said to be externally enforced if it requires the intervention of a third party to enforce compliance.

CONTRACTING PHASE

During the contracting phase of a contractual relationship, the players negotiate terms, obligations and payoffs. The result may be an explicit, written agreement, such as an international trade treaty between countries or a formal document that defines management-labor relations. A contract may also be less formal tacit or verbal understanding, such as might define the obligations of family members. In addition to defining the obligations and payoffs of the contracting parties, contract negotiations must also take into account the dynamics of the bargaining process, which were discussed in the previous chapter.

To illustrate the basic elements of a contractual relationship, consider the following example of a simple loan contract, which is depicted in Figure 14.1. In this game, player 1 (the lender) decides to lend or not lend an amount (L) in exchange for a promise by player 2 (the borrower) to repay L plus simple

Figure 14.1

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interest (iL) in one year. Player 2 promises to use the loan to finance a capital investment with an expected rate of return of r. To guarantee repayment of principal, the loan is fully collateralized.

In the lending game depicted in Figure 14.1, we assume that the borrower has the ability to repay the loan with interest, but may not have the willingness to do so. In the literature dealing with asymmetric information, this is a moral hazard problem, which is the risk (hazard) that the borrower will engage in an activity (default) that is undesirable (immoral) from the lender’s perspective. We also assume that the players are risk averse and that a dollar received yields the same marginal utility to both players.

The game begins when player 1 decides to lend or not lend. If player 1 does not lend, the game ends and the payoff to both players is $0. If player 1 lends, player 2 decides whether to repay or default in the second stage. If the loan is nominally serviced, player 1 earns iL and player 2’s earns (r – i) L > 0. If player 2 defaults, player 1 loses interest earnings (–iL), but does not lose principal because the loan is collateralized. The payoff to player 2 is rL, which is the return on the investment.

IMPLEMENTATION PHASE

Once the terms of the contract are negotiated and specified in the contract is written, the next step is execution and enforcement. In this section, we will examine two basic methods of enforcement in our loan contract example: Self-enforcement and external enforcement.

Self-enforcement

A contract is self-enforced if it is in both players best interest to abide by the terms of the contract. In the lending game depicted in Figure 14.1, the

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contract will be self-enforced provided that the strategy profile {lend → repay} is a subgame-perfect equilibrium, which is possible if and only if

( ) r i L r− ≥ L. (14.1)

Unfortunately, condition (14.1) can only be satisfied when the lender charges a zero or negative interest rate! In other words, the contract is selfenforcing only if the lender subsidizes the borrower’s investment. For any positive interest rate, it will be in the borrower’s best interest to default. For any positive interest rate, the subgame-perfect equilibrium is {not lend}, in which case a profitable investment opportunity is lost.

To make the lending game more concrete, suppose that player 2 wants to borrow $100 at 5 percent simple interest to finance an investment that promises a 10 percent rate return. This lending game is depicted in Figure 14.2. Based on the payoffs, it is in the borrower’s best interest to default if the loan is made. Thus, it is in the lenders best interest not to lend. The subgameperfect equilibrium for this game is {Not lend}.

External Enforcement

In the game depicted in Figure 14.1, self-enforcement will be ineffective unless the lender subsidizes the borrower’s investment. What role can the courts play in the enforcement of the loan contract? One thing that the court can do is to step in and compel one party to pay the other party damages in the event of a default. In this case, the court will remedy the situation by requiring the borrower to transfer an amount (α) to the lender. This revised lending game is depicted in Figure 14.3.

Figure 14.2

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Depending on the amount of the transfer, external enforcement changes the outcome by altering the payoffs. To keep the lender from defaulting, the court-ordered transfer must satisfy the condition

a ≥ iL. (14.2)

Suppose, for example, that it is known to both players that the court will order the borrower to pay the lender α = $6 in the event of default. In this case, the payoff to the borrower is rL– α = $4. This new situation is depicted in Figure 14.4. The reader should verify that the subgame-perfect equilibrium is {Lend → Repay}. By altering the payoffs, the threat of a court-imposed transfer has made self-enforcement desirable. Note that in this game, the size of the transfer was set to alter the borrower’s behavior—not to protect the lender. In the unlikely event of default, the transfer does not protect the borrower from incurring opportunity costs.

Figure 14.3

Figure 14.4

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In reality, intervention by the court does not always lead to a transfer between contracting parties since high legal costs impose a transfer on both players. As a result, litigants frequently negotiate an out-of-court settlement that produces an economically inefficient outcome.

SOLvEd ExERCISE

Several years ago the U.S. Army requested proposals from its top contractors to develop the Hell Cat armored helicopter gunship. Although Sikorsky Aircraft was expected to win the competition, the contract was eventually awarded to a joint venture between Dynamic Diesel and Sea-Air Systems. The joint venture was unusual because of the fierce competitive rivalry that existed between these two companies over the past five decades. After the contract with the U.S. Army was signed, each company simultaneously, and independently, decides to fully invest (FI) or under-invest (UI) in the project. The normal form for this one-time, noncooperative static game is depicted in Figure 14.5. Assume that payoffs are in millions of dollars and that transfers between players are possible.

a. What conditions must be satisfied for the value of this joint venture to be maximized? b. Under what conditions would this contract be self-enforced? c. Suppose that the U.S. Army relied upon the courts to enforce this contract.

What conditions must be satisfied with respect to the size of court-enforced transfers to produce an economically efficient outcome?

Solution

a. For the value of the joint venture to be maximized, it must be the case that a + b > c + d, a + b > e + f, and a + b > 0. b. This contract will be self-enforced if it is in the players’ best interest to play the Nash equilibrium strategy profile is {FI, FI}. For this to happen,

Figure 14.5

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it must be the case that a ≥ c and b ≥ f. If these conditions are not satisfied, enforcement by a third party, such as the courts, may be required. c. The players in the contract game depicted in Figure 14.5 have an incentive to defect if c > a and f > b, in which case the Nash equilibrium strategy profile is {UI, UI}. Now, consider the revised contract game depicted in

Figure 14.6 in which α and β represent the values of court-order transfers.

In order for the external enforcement to induce the economically efficient outcome {FI, FI}, the court-ordered transfers must satisfy the conditions α ≥ c – a and β ≥ f – b.

Complete Contracts with Full Verifiability

We will now change the nature of the game depicted in Figure 14.3 by allowing the parties to incorporate the size and type of transfer in the contract. Whereas external enforcement relies on the court to both specify and enforce the amount of the transfer, a complete contract only requires the court to enforce a transfer previously agreed to by the players. We will assume that the court has complete information regarding the details of the loan transaction, the players, strategies, payoffs, and the transfer. This informational requirement, which is referred to as full verifiability, means that the court has the evidence it requires to enforce the transfer provision of the contract.

An example of a complete contract is a mortgage in which property purchased with the proceeds of the loan is used as collateral in the event of default. Typically, the size of the loan is less than the value of the property put up as collateral. In the event of default, the lender seizes the collateral, which is then sold to repay the loan. Provided that the loan is not “underwater,” the lender will sell the collateral to pay off the outstanding balance.2 If the proceeds from the sale of collateral is greater than the loan, the difference is returned to the borrower.

Suppose that in our example, the transfer specified in the loan contract is α = iL = $5. This new game is depicted in Figure 14.7. Unlike the situation

Figure 14.6

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Figure 14.7

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depicted in Figure 14.4, the negotiated transfer not only encourages selfenforcement, but in the unlikely event of default, the lender is fully protected.

Complete Contracts with Limited Verifiability

Unfortunately, in some cases the court may not have complete information regarding the underlying loan transaction. For example, the court may not have the expertise necessary to assess the market value of the collateral, verify the expected return on the investment (r), or determine whether the borrower used the loan proceeds as intended (a moral hazard problem). This condition of incomplete information is referred to as limited verifiability.

In the case of limited verifiability, it is difficult for the court to accurately determine a transfer amount that will result in an efficient outcome. One solution is for the players to allow the court to impose a transfer based upon the limited information that it is able to verify. Unfortunately, this makes it difficult for the players to write a contract that guarantees an efficient outcome.

BREACH REMEdIES

We have thus far assumed that contracts are complete in that they fully reflect deliberate negotiations between the contracting parties and account for every possible contingency. In many real world situations, however, contracts are incomplete in the sense that they only reflect how the players intend to behave. Preparing a contract is time consuming, and costly. Since it may be difficult or impossible to anticipate every possible outcome, the contracting

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parties frequently rely on the courts to clarify grey areas in the event of a breach of contract, which occurs when a party to a contract fails to perform, or refuses to perform, a specified obligation.

In the event of a breach, the injured party, or plaintiff, may seek courtordered damages from the injurer, or defendant. Once the court has established liability, it may then impose a breach remedy, which may take the form of a transfer of money or some other form of compensation from the defendant to the plaintiff. Since it may be difficult in incomplete contracts to fully verify damages, the court may provide the defendant with relief based of certain legal principles, such as expectation damages, reliance damages, and restitution damages.3

Expectation damages

Breach remedies based on the legal principle of expectation damages attempt to compensate the plaintiff by ordering the defendant to pay damages equivalent to the amount that the plaintiff would have received had the contract been fulfilled. This is the situation depicted in Figure 14.3 where the transfer is α = iL. If expectation damages are correctly specified, the borrower will not have an incentive to breach the contract.

Expectation damages will likely result in the same efficient outcome as when the contract is completely specified. This is because the borrower is indifferent between the repay and default payoffs. It is unlikely, however, that the courts will have sufficient information to correctly specify expectation damages. If this information had been available, the players would have written a complete contract. The court not only has to determine who was responsible for the breach, the precise value of the resulting payoffs, and what the payoffs would have been had the contract not been breached.

Reliance damages

An alternative to expectation damages as a breach remedy is reliance damages, which is a court-ordered transfer designed to restore the plaintiff to a condition that would have prevailed in the absence of a contract. Reliance damages include any expenses that may have been incurred by the plaintiff who did not anticipate a breach of contract.

Determining the amount of reliance can be problematic since it involves the determining the value of the plaintiff’s next best alternative activity had the contract not been signed. Moreover, reliance damages must be sensitive to the problem at hand. The amount of the transfer must be sufficiently large to encourage subgame perfection.

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Restitution damages

Another example of a breach remedy is restitution damages, which is designed to negate undue enrichment by the defendant resulting from the breach relative to what would have prevailed in the absence of a contract. In terms of Figure 14.1, the restitution damages imply a transfer in the lending game of α = rL. As in the case of reliance damages, efficient restitution damages assumes that in the event of a breach the courts are able to accurately determine the plaintiff’s expenditures, the value of the plaintiff’s foregone opportunities, and the value of the defendant’s undue enrichment.

CHAPTER ExERCISES

14.1 Explain the difference between a contractual relationship and a contracting environment. 14.2 Legally enforceable contracts are always necessary for a market transaction to take place. Do you agree with this statement? Explain. 14.3 Under what circumstances will a contract be self-enforced? When is it necessary to externally enforce a contract? 14.4 What is the role of the courts when enforcing a complete contract that is fully verifiable? 14.5 What problems are confronted by the courts when attempting to enforce a complete contract with limited verifiability? 14.6 When the parties to a contract are reasonably certain that the victim of a breach has legal recourse to recover damages, it is possible to structure a contract that gives players an incentive to adopt strategies that are mutually and socially beneficial. Why? 14.7 When it is difficult to fully verify damages, the court-imposed breach remedies may be based on legal principles. Name three such legal principles, and explain how they differ. 14.8 Consider the lending game depicted in Figure 14.1. Suppose that the payoff to the borrower in the event of default is rL – R, where R represents the present value of the borrower’s reputation in credit markets. Loss of reputation increases the borrower’s future financing costs. For what values of R will the loan contract be self-enforcing? 14.9 A lender has to decide whether to extend a $1,000 loan in exchange for a promise by the borrower to repay the loan and 10 percent simple interest in one year. The borrower plans to invest the proceeds of the loan with a certain 25 percent rate of return. The lender believes there is a 90 percent chance that the loan will be repaid. What is the subgame-perfect equilibrium for this lending game?

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14.10 Consider the game depicted in following figure. Suppose that two companies (Firm 1 and Firm 2) form a joint venture to develop a new product. The parties write a contract that obligates both parties to fully invest in the project. When the contract is implemented, each company simultaneously, and independently, decides to fully invest (FI) or under-invest (UI). a. Is this game self-enforcing? Why? b. What is the normal form of this game if the court imposes breach remedies under the legal principle of expectation damages? c. Suppose that the companies write a complete contract with limited verifiability in which the court can only determine whether underinvestment has occurred, but not which company has underinvested. Is there a contract that will result in an efficient outcome?

14.11 Consider the game depicted in the following figure. Two companies (Firm 1 and Firm 2) form a joint venture to develop a new product. The players write a contract that obligates both parties to fully invest in the project, which relies on the courts to impose a remedy in the event of a breach. At the outset of the game, each company simultaneously, and independently, decides to fully invest (FI) or underinvest (UI). a. What is the normal form of this game with court-imposed expectation damages that encourages the strategy profile {FI, FI}? Explain. b. What is the normal form of this game with court-imposed reliance damages that encourages the strategy profile {FI, FI}? Explain. c. What is the normal form of this game with court-imposed restitution damages that encourages the strategy profile {FI, FI}? Explain. d. Suppose that each player incurs court costs (c) in the event of litigation following a breach of contract. What is the normal form of this game if the court imposes expectation damages? e. What values for c will the plaintiff have an incentive to sue?

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NOTES

1. Samuel Goldwyn (1882–1974), founder of Metro-Goldwyn-Mayer, is reported to have quipped: “A verbal agreement isn’t worth the paper it’s written on.” 2. A mortgage is said to be “underwater” when the outstanding balance on the loan is greater than the value of the collateral. 3. See Steven Shavell (1980) for an analysis of the breach remedies examined in this section.