Scott Im Ch09

CHAPTER 9 AN ANALYSIS OF CONFLICT 9.1

Overview

9.2

Understanding Game Theory

9.3

A Non-Cooperative Game Model of Manager-Investor Conflict 9.3.1 Summary

9.4

Some Models of Cooperative Game Theory 9.4.1 Introduction 9.4.2 Agency Theory: An Employment Contract Between Firm Owner and Manager

9.5

Manager’s Information Advantage 9.5.1 Earnings Management 9.5.2 Controlling Earnings Management

9.6

Discussion and Summary

9.7

Agency Theory: A Bondholder-Manager Lending Contract

9.8

Implications of Agency Theory for Accounting 9.8.1 Holmström’s Agency Model 9.8.2 Rigidity of Contracts

9.9

Reconciliation of Efficient Securities Market Theory with Economic Consequences

9.10

Conclusions on the Analysis of Conflict

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LEARNING OBJECTIVES AND SUGGESTED TEACHING APPROACHES 1.

To Introduce Fundamental Concepts of Non-Cooperative Game Theory

My objectives here are quite limited, being confined to developing the intuition underlying a simple, one-shot, prisoner’s dilemma type of game. I concentrate on the concept of strategic decision-making where, for each decision maker, the possible actions of a rational opponent need to be taken into account. Using the Nash equilibrium concept, I show how game theory can model and predict the outcome of conflict situations. The idea is to demonstrate that investors and managers are in a conflict situation since the manager’s interest in financial reporting can conflict with what is in the investor’s best interests. As a result, capital markets will not work as well as they could. This is captured in the game by the Nash equilibrium outcome leaving each party less well off than the cooperative solution. To attain the cooperative solution, I suggest that a standard setting body, by controlling the payoffs of the game, can influence its outcome. Instructors may wish to motivate this suggestion by picking up on the brief interpretation of Example 9.1 into the Enron and WorldCom episodes, where these firms and investors ended up in the Nash equilibrium. Subsequent attempts by regulators and professional accounting bodies to restore investor confidence can be regarded (hopefully) as a move back to the cooperative outcome. The purpose of the brief outline of Darrough and Stoughton (1990) in Section 9.3 is to further motivate the game theory topic by describing how it can be applied to predict the outcome of another type of financial reporting conflict, namely the tradeoff faced by a manager between the role of financial reporting to reduce cost of capital and its role in deterring entry into the industry. I do not assign the Darrough and Stoughton paper itself. Instructors who wish to spend more time on game theory could usefully do so. Since Darrough and Stoughton, numerous researchers have studied the conflict between disclosure, threat of entry, and cost of capital. However, additional game theoretic concepts would need to be

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developed beyond the simple prisoner’s dilemma example in the text. The Darrough and Stoughton model is a 2-stage entry game with asymmetric information. For additional motivation, I usually hand out in class and discuss one or more articles from the financial press relating to game theory. Some interesting articles are: •

“It’s only a game,” The Economist, June 15, 1996, p. 57.

•

“Nobel in Economics is Awarded to Three for Pioneering Work in Game Theory,” The Wall Street Journal, October 12, 1994, p. B12.

•

“How game theory rewrote all the rules, “ Business Week, October 24, 1994, p. 44.

• 2.

“Businessman’s dilemma,” Forbes, October 11, 1993, pp. 107-109.

To Introduce Fundamental Concepts of Agency Theory

In this edition, I have rewritten the agency material to bring it up to date. The development is now slightly more complex, although I have retained the intuitive, stepby-step, example-based approach of earlier editions. The main change is that the payoff is not realized until after the single-period contract expires. However, the agent must be compensated at period end. This allows net income to be viewed as a performance measure upon which compensation is based, leading naturally to consideration of the ability of net income to predict the payoff, and the properties it needs to be a good predictor. In earlier editions, net income was the payoff. I have also introduced concepts of biased reporting and earnings management, although, depending on the level and interests of the class, instructors should tread carefully here. I have designed the chapter, and subsequent chapters, so that some of this material can be skipped. My objective in introducing this material is to better integrate the theory into the coverage of executive compensation and earnings management in Chapters 10 and 11. In particular, I show in Example 9.5 that uncontrolled earnings management results in a very inefficient contract. However,

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Example 9.7 shows that that if it is controlled (but not eliminated) by GAAP, earnings management can be “good,” in the sense that a contract that allows a degree of earnings management can be more efficient than one that motivates the manager to tell the truth. This leads into the discussion of good versus bad earnings management in Chapter 11. However, as mentioned, Chapter 11 stands on its own and does not require the optional material in this chapter. Since most students will not have been exposed to agency theory before, I suggest working through Examples 9.2, 9.3 and 9.4, and perhaps Example 9.5, in class. My main goal is that the students understand why compensating a manager based on some measure of his/her performance is usually desirable when moral hazard is present, and are aware of the properties that net income needs to control moral hazard efficiently. The risk-sharing aspect of agency contracts is worth emphasizing. The main point is that to motivate effort, the manager must bear compensation risk—a fixed salary does not provide any effort incentive. Instructors may wish to challenge this point, however. What about ethics? Should a manager shirk on his/her employer? I counter this argument by asking what would happen if I cancelled the final exam. What about reputation? While perhaps not completely convincing, I counter this argument by suggesting that managers may be able to disguise shirking and preserve their reputations by earnings management. Nevertheless, the reason I suggest discussion of risk-sharing is that it supports the point made several times in the book that new accounting standards that increase the volatility of earnings will be objected to by managers. Since the manager is assumed risk averse, increased compensation (and debt covenant) risk lowers the manager’s expected utility. Appreciation of the manager’s legitimate concern about risk helps students to understand the controversies surrounding many accounting standards. I usually let the students read Example 9.8 for themselves, dealing with a manager/lender moral hazard problem.

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I do not assign Holmström’s well-known 1979 paper, but I use the discussion of it in Section 9.8.1 to develop several implications of agency theory for accounting: •

Is net income sufficiently observable that it can serve as a basis for manager compensation? GAAP and the audit are the vehicles that give net income sufficient observability that parties are willing to use it in contracts. Although financial reporting disasters such as Enron may threaten this argument, a theme of this book is that the contracting role for net income is equally as important as its role in informing investors. •

I suggest to the class that historical cost-based net income may be more informative about manager effort (and hence a more efficient performance measure on which to base manager compensation) than net income determined under a fair value-based measurement perspective. This leads to development of the concepts of sensitivity and precision of a performance measure, which are developed more fully in Chapter 10. The point I want to get across is that historical cost-based net income is less sensitive but more precise than fair value-based net income. Thus, the accountant faces a tradeoff between these 2 desirable qualities.

•

Holmström’s main contribution in his 1979 paper was his informativeness condition, that is, the condition under which basing the agent’s compensation on a second variable, in addition to the payoff itself, would increase contracting efficiency. This leads to a suggestion to base managerial compensation on both net income and share price.

•

It is important to point out the rigid nature of contracts, once they are signed, and to discuss the reasons for rigidity. Otherwise, students tend to ask what the fuss is all about when GAAP changes. Why not just amend the contract when this happens? Contract rigidity is crucial for accounting policies to have economic consequences. The Mosaic Group vignette in Section 9.8.2 is useful in bringing out the consequences of rigidity, and

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convincing students that the implications of contracts (debt covenants in this case) for accounting matter. If further intuition for and motivation of agency theory are desired, I recommend an interesting and readable article which appeared in the Harvard Business School Bulletin, Vol. 59, No.2 (December, 1983), pp. 62-71, by N. Jackson, entitled “Looking Out for No. 2.” It is rather old now, but still worth looking at. 3.

To Motivate Agency Theory to Accountants

Since the theory may be new to many students, I work to convince them it is relevant to their future careers. Some of the points I bring out are; • Agency relationships are very common. I sometimes discuss examples such as hockey players, and ask why they are motivated to work hard. Presumably their effort is observable, so that they receive primarily salaries. I also ask about visiting a lawyer or doctor, and ask how one can be sure the professional will work hard on the client’s behalf (contingent fees? lawyer wins case or not? patient gets better or not?). Asking what motivates an auditor to work hard also draws interesting replies. The point here is that agent effort is important to everyone, and the extent to which effort is observable influences how the agent is motivated and compensated in predictable ways. • I suggest to the students that in their careers they will find that much attention is given to accounting policy choice and they will be arguing with managers about such choices. Indeed, some of them will eventually be managers. Agency theory helps us to understand how managers view accounting policies. For example, the fact that managers bear considerable risk helps explain their often-negative reaction to new accounting policies, such as fair value. • I use Holström’s informativeness condition to point out that accounting competes with share price as a performance measure. The demand for accountants’ services will fall if net income is squeezed out of compensation and debt contracts. Students should be aware of the properties a good performance

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measure should have, and that these properties are not necessarily the same as those needed to inform investors. 4.

To Reconcile Economic Consequences with Efficient Securities Markets

Finally, I use the prediction from agency theory that important classes of contracts will be based on accounting variables, in conjunction with contract rigidity, to emphasize the argument in the text that accounting policies can have economic consequences even if securities markets are efficient. By this time, students have no problem in accepting this argument (or else I have worn them out). I should note, however, that I back off this argument somewhat in Section 11.6.2, by suggesting that another reason for economic consequences arises if managers do not accept securities market efficiency. Then, they may feel they can influence the securities market by accounting policy choice and will object if accountants try to constrain those choices.

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SUGGESTED SOLUTIONS TO QUESTIONS AND PROBLEMS 1.

The manager’s effort is usually unobservable to owners because of the complex and broadly-defined nature of manager effort. As a result, it is effectively impossible in most situations to observe whether the manager is working hard or shirking. If the manager receives a straight salary, his/her compensation does not depend on the amount of effort exerted. Since managers are assumed to be rational and effort-averse in agency theory, their utility will be maximized by working as little as possible, in a single period contract. An alternate answer is to point out that if the manager receives a straight salary, he/she bears no compensation risk. Compensation risk is necessary if hard work is to be motivated. Note: A superior answer will suggest that an ethical manager may work hard anyway. Also, in a multi-period contract, reputation considerations may motivate effort.

2.

The reason is that the payoffs from current effort often take a long time. As a result, the accounting system reacts by estimating the payoffs (i.e., accruals) if this can be done with reasonable reliability. If not, we have recognition lag. (Accounting for R&D and environmental liabilities are examples.) Because estimation of the future cash flows from current manager effort is often too unreliable, the accountant waits until reasonably objective evidence of realization is available before entering these payoffs into the accounting system.

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Less noise means greater precision of net income as a performance measure. Greater precision, other things equal, means greater accuracy in measuring the ultimate payoff. This reduces the manager’s compensation risk, resulting in a more efficient contract. Ways that accountants can reduce noise include: •

Conservative accounting, such as historical cost. This increases precision because historical cost relies less on estimates than, say, fair value accounting.

•

Use of market values, if available. These increase precision because, if markets work reasonably well, current value provides an unbiased estimate of future market value, hence of payoff.

•

Use of models (e.g., Black/Scholes). These may enable reasonably precise estimates of fair values, hence of future payoffs. (However, models may not capture the full complexity of all valuation problems, and their outputs are only as good as their parameter inputs.)

•

Use of large data bases, and information technology to exploit their information potential. These may enable precise estimates of future cash flows, for example for pension and OPEB liabilities.

4.

The basic reason for debt covenants is the moral hazard problem between manager and lender. As a result, lenders demand a high interest rate to protect themselves from the expected opportunistic manager behaviour (e.g., excessive dividends or additional borrowing). To lower the interest rate demanded, the manager may commit not to engage in this behaviour. Debt covenants based on accounting variables are a credible way to do this since the lender can rely on GAAP and auditing to prevent undue manager interference in the covenant levels.

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The reason why net income is not fully informative about manager effort is because the full payoff from current manager effort is not realized until some time in the future. As a result, net income contains accruals to estimate these payoffs and/or recognition lag. Both of these effects reduce the ability of current net income to precisely measure manager performance. Another reason is that net income may be biased (i.e., managed) by the manager to disguise shirking. Example 9.5 illustrates this possibility. The compensation plan designer may add another performance measure, such as share price performance, to the compensation plan. Assuming that share price meets the requirements of Holmström (1979) (see Note 14), the 2 performance measures are more informative than either one alone. Note: If the student has covered the optional material in this chapter, another answer is that the plan designer may rely on GAAP and auditing to generate a net income number sufficiently informative so as to control the manager’s tendency to shirk. This is illustrated by Example 9.7.

6.

Sensitivity is the rate at which the expected value of a performance measure increases as the manager works harder, or decreases as the manager shirks. Precision is the ability of a performance to predict the payoff with relatively high probability. It is measured as the reciprocal of the variance of the noise in the performance measure. When a performance measure is precise, it is unlikely that it will differ substantially from the payoff. Accountants can increase sensitivity by adopting fair value accounting (for example, for R&D and RRA). This increases sensitivity because fair values capture more of the results of current manager effort than more conservative accounting policies such as historical cost. That is, if the manager works harder, the results of this effort show up in fair value-based net income whereas they

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show up less so or not at all under conservative accounting (e.g., R&D is written off currently, and RRA is given as supplementary information only.) Accountants can increase precision by adopting conservative accounting, such as historical cost. This increases precision because fair values are subject to noise, such as from economy-wide events, that affects current values of assets and liabilities. Conservative accounting values are less subject to these effects. Less noise means greater precision. These two qualities have to be traded off because attempts to increase sensitivity (such as fair value accounting) reduce precision, and vice versa.

7.

This $25 net income could happen if some state of nature that was not anticipated was realized during the year. This could happen, for example, if a new accounting standard changes the way net income is calculated. Alternatively, any other unanticipated event, such as a new competitor entering the industry, could reduce profits. A contract that does not anticipate all possible state realizations is incomplete. Possible manager reactions: •

Ask to renegotiate the contract. This may be difficult, however, due to contract rigidity.

•

Manage earnings upward to restore compensation to anticipated amount.

•

If a new accounting standard is the reason, intervene in the standardsetting process, to try to secure reversal or modification of the new standard.

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This is a version of the “owner rents firm to the manager” or tenant farming scenario described in Section 9.4.2. Here, we can think of a firm as the principal, or employer, with the employee as the agent or manager. The employer pays a fixed rental to the employee for the move. The employee is then motivated to move as cheaply as possible, since he/she keeps any excess. Note that the employee also bears the risk of loss or damage during the move. Thus, the employee does all the work and bears all the risk. This also illustrates how the employee’s decision about how much effort to exert in moving is internalized. By paying a fixed allowance, the employer does not care how hard the employee works on the move. This is internalized to the employee. Under the previous arrangement, the employer did care how hard the employee worked on the move. The harder the employee worked, the lower the moving costs paid to the moving company. However, with the employer paying the moving costs, an effort-averse employee would obviously prefer to exert no effort (a moral hazard problem), let the moving company do all the work and bear all the risk, and send the bill to the employer. U-Haul’s offer to reimburse for oil follows from the fact that, since the employee does not own the moving truck, he/she has no incentive to look after it (another moral hazard problem). By offering to pay for oil, U-Haul reduces the incentive for the employee to shirk on his/her obligation to keep the oil level up.

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a.

The predicted outcome is that both parties play strong.

b.

Yes, (strong, strong) is a Nash equilibrium. Each player has an incentive

to play strong, given that the other player chooses strong. For example, if the FASB plays strong, the corporations receive a higher payoff from playing strong (12) than playing cooperate (8). Similarly, if the corporations play strong, the FASB is better off to also play strong since its payoff is lowered from 15 to 10 if it cooperates. Consequently, (strong, strong) is a Nash equilibrium. c.

Both parties would be better off if they cooperated, rather than each

playing strong. However, if the corporations play cooperate, the FASB will reason it would be better off to play strong, thereby raising its payoff from 30 to 40. In the absence of a binding agreement that would force the FASB to cooperate, the (cooperate, cooperate) strategy is likely to break down. This strategy is not a Nash equilibrium.

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The cash flows to each player are as shown in the payoff table: Management Do not manage

Manage

earnings

earnings

Bonus plan

100, 50

80, 60

No bonus

110, 30

70, 30

Shareholders

plan

The first number in each box represents the payoff to shareholders. Note that cash flows to shareholders are net of compensation paid to management. Note also that if management manages earnings, the cash flows to shareholders are less than if management does not manage earnings. This is because under the manage earnings alternative, management works less hard–it gets reported earnings (but not cash flows) up by manipulating accruals rather than by working hard. b.

A Nash equilibrium is (bonus plan, manage earnings).

Note that the manager is indifferent between managing and not managing earnings if the shareholders play bonus plan. If we assume that management would then choose the pure strategy desired by the shareholders, a second Nash equilibrium is (no bonus plan, do not manage earnings). c.

The main advantage is that the conflict situation between management

and shareholders is formally modeled. This gives us a better understanding of the process of earnings management, because both management’s reaction to the shareholders’ bonus plan decision and the shareholders’ reaction to

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management’s earnings management decision are simultaneously taken into account. In single-person decision theory, in deciding on which act to take, shareholders would have to assign probabilities to management’s possible actions of managing or not managing earnings. Similarly, in deciding whether not to manage earnings, management would have to assign probabilities to the granting /non-granting of the bonus plan. That is, managing/not managing earnings and granting/not granting the bonus plan, respectively, are states of nature in a decision theoretic formulation of the problem. In a valid single-person decision problem, state probabilities must not depend on the action chosen. This is not the case here, since the action chosen by the shareholders will certainly affect the probability of what management does, and vice versa. That is, a singleperson decision theory formulation does not capture the players’ strategic reaction to the other player’s action choice. Thus, predictions about what might happen here, if based on the single-person decision theory model, are unlikely to be as accurate as if based on the game theory model, and we would be less likely to understand what is really going on. Note: A complication with the game-theory approach, however, is that there may be more than one Nash equilibrium. Then, the prediction of the game-theory approach is less clear.

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The Nash equilibrium is do not invest, work for manager. This is the only

strategy pair such that, given the strategy choice of the other player, neither player has an incentive to change strategies. b.

The cooperative solution is invest, work for investor. In this strategy, both

players are better off than in the Nash equilibrium. The cooperative solution is unlikely in a single play because if the investor invests, the auditor will move to work for manager. Realizing this, the investor does not invest. c.

Three possible ways to attain the cooperative solution: •

The investor and auditor could enter into a binding agreement to play the cooperative strategy.

•

Ethical behaviour by the auditor, reinforced by the auditor’s professional association and longer-run reputation considerations, may motivate the auditor to work for the investor despite the higher one-shot payoff of working for the manager.

•

Change the payoffs of the game. For example, if the investor invests, a penalty of 4 for working for manager would lower the auditor’s payoff to 2. Then, the auditor would move to work for investor. Increased regulations following the Enron and WorldCom scandals, such as Sarbanes-Oxley, may have this effect.

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Denote working hard by a1 and shirking by a2. Yvonne’s expected utility of

each act is: EUm(a1 ) = 0.9 × (100 + .10 × 2,000)1/2 + 0.1 × (100 + .10 × 900)1/2 – 4 = 0.9 × (300)1/2 + 0.1 × (190)1/2 – 4 = 0.9 × 17.32 + 0.1 × 13.78 – 4 = 15.59 + 1.38 – 4 = 12.97 EUm(a2 ) = 0.1 × 17.32 + 0.9 × 13.78 – 1.1 = 1.73 + 12.40 – 1.1 = 13.03 Yvonne accepts because her expected utility is greater than her reservation utility. She will shirk. b.

Under the new contract, Yvonne’s expected utility of each act is:

EUm(a1) = 0.9 × (52.30 + .0921 × 2,000)1/2 + 0.1 (52.30 + .0921 × 900)1/2 – 4 = 0.9 × (236.50)1/2 + 0.1 × (135.19)1/2 – 4 = 0.9 × 15.38 + 0.1 × 11.63 – 4 = 13.84 + 1.16 – 4 = 11 EUm(a2) = 0.1 × 15.38 + 0.9 × 11.63 – 1.1 = 1.54 + 10.47 – 1.1 = 10.91 Yvonne hesitates because her expected utility is lower than under the original contract. However, since she can attain her reservation utility she does accept. She will work hard.

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Denote Pierre’s utility by EUO:

EUO (original contract) = 0.1 × (2,000 - 100 200) + 0.9 × (900 - 100 - 90) = 0.1 × 1700 + 0.9 × 710 = 170 + 639 = 809

EUO (new contract) = 0.9 × (2,000 - 52.30 - 184.20) + 0.1 × (900 - 52.30 - 82.89) = 0.9 × 1763.50 + 0.1 × 764.81 = 1587.15 + 76.48 = 1663.63 The new contract yields Pierre higher expected utility. The new contract is thus more efficient. This is both because it now motivates Yvonne to work hard, and because it gives her her reservation utility. The old contract gave her more than her reservation utility.

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The payoff table is as follows: Manager’s Act a1 (work hard) Net Inc.

Probability

a2 (shirk) Net Inc.

Probability

High net income

$500

0 .7

$500

0.2

Low net income

$200

0.3

$200

0.8

a.

The manager’s expected utility for each act is: EU(a1) = 0.7 41 + .2 × 500 + 0.3 41 + .2 × 200 - 2 = 0 .7 × 11.87 + 0 .3 × 9 - 2 = 8.31 + 2.70 - 2 = 9.01 EU(a2) = 0.2 × 11.87 + 0.8 × 9 - 0 = 2.37 + 7.20 = 9.57

The manager will take a2. b.

EU(a1) = 0.7 0.3 × 500 + 0 .3 0.3 × 200 - 2 = 0.7 × 12.25 + 0.3 × 7.75 - 2

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EU(a2) = 0.2 × 12.25 + 0.8 × 7.75 - 0 = 2.45 + 6.20 = 8.65 The manager will now take a1. Note: It is assumed in parts a and b that the prospective manager’s reservation utility is met. c.

Yes. The elimination of salary plus higher profit percentage in b provides

sufficiently more expected utility of compensation that it overcomes the disutility of working hard. Alternatively, the contract in b imposes more risk on the manager. This motivates her to work hard. d.

The advantage of using two performance measures was demonstrated by

Holmström (1979). A second measure increases contracting efficiency provided that the second measure tells us something about the manager’s effort beyond the first measure. This would seem to be the case for share price since, despite its volatility, share price on an efficient market reflects all publicly available information about the firm. That is, share price draws on a larger set of information than net income, which is constrained by reliability considerations from timely reflection of the payoff from manager effort such as R&D, capital investment, plans for mergers, growth expectations, environmental liabilities, prospective lawsuits, etc.

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Let the proportion of net income be x. Then we want EU m (a1 ) = 0.75 725 x + 0.25 0 − 2 = 6 = 0.75 × 26.93 x + 0 − 2 = 6 = 20.20 x = 8 from which 8 x= = .40 20.20 x = .16

b.

To check, this profit share yields

EU m (a1 ) = 0.75 .16 × 725 − 2 = 0.75 116 − 2 = 0.75 × 10.77 − 2 = 8.08 − 2 ≈6 If Lily shirks with this profit share, her expected utility is

EU m (a 2 ) = 0.20 .16 × 725 + 0.80 0 − 1 = 0.20 116 − 1 = 0.20 × 10.77 − 1 = 2.15 − 1 = 1.15 Consequently, Lily will work hard.

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If Lily manages earnings and shirks in year 1, her expected utility is

EU m (a 2 ) = .16 × 725 − 1 = 116 − 1 = 10.77 − 1 = 9.77 If she does not manage earnings, and works hard, her expected utility, from b is 6. Thus Lily would be better off in year 1 to manage earnings and shirk. d.

Lily may not manage earnings, despite the temptation to do so, because

•

Tom may hire an auditor. If so, the earnings management may be revealed.

•

Accruals reverse. This will make it more difficult to manage earnings in future years, should her contract be renewed.

•

Lily may be concerned about damage to her reputation if the opportunistic earnings management is discovered. This would lower her reservation utility.

•

Ethical considerations.

Note: Two additional reasons can be suggested from material covered in Chapter 10 (Section 10.2):

•

Internal monitoring. Subordinates, who want the manager’s job, may whistle-blow (Fama, (1980)).

•

Co-workers may threaten to shirk next period if the manager shirks this period (Arya, Fellingham and Glover (1997)).

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If Marie works hard (a1), her expected utility is: EU(a1) = 0.7 (20 + .05 × 280)1/2 + 0.3 (20 + .05 × 60)1/2 – 2.00 = 0.7 × 341/2 + 0.3 × 231/2 – 2.00 = 0.7 × 5.83 + 0.3 × 4.80 – 2.00 = 4.08 + 1.44 – 2.00 = 3.52

If Marie shirks (a2), her expected utility is: EU(a2) = 0.2 × 5.83+ 0.8 × 4.80 – 1.60 = 1.17 + 3.84 – 1.60 = 3.41 Marie will work hard. She accepts immediately because by working hard she receives more than her reservation utility of 3.41. b.

The bank manager is concerned that if the low earnings state happens (as

it will with probability 0.3), Marie, who will control the store’s accounting system while Henri is gone, may manage earnings upwards, or simply falsely report high earnings, so as to receive the high compensation. An audit according to GAAP will protect Henri against this possibility. c.

Marie’s expected utilities are now: EU(a1) = 0.7 (20 + .05 × 266)1/2 + 0.3 (20 + .05 × 20)1/2 – 2.00 = 0.7 × 33.301/2 + 0.3 × 211/2 – 2.00 = 0.7 × 5.77 + 0.3 × 4.58 – 2.00 = 4.04 + 1.37 – 2.00 = 5.41 – 2.00 = 3.41

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EU(a2) = 0.2 × 5.77 + 0.8 × 4.58 – 1.60 = 1.15 + 3.66 – 1.60 = 4.81 – 1.60 = 3.21 Marie will continue to work hard. However, she will be concerned about the new accounting standard, because she now receives only her reservation utility of 3.41, whereas before she received 3.52.

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The (net) payoff table is: State

Payoff

21

$40.00

22

0.00

23

-500.00

Expected payoff is 0.80 × 40 + 0.18 × 0 + 0.02 × -500 = 32 - 10. = $22.00 Expected rate of return is thus 22/500 = 4.4% Since this is less than 6%, Mr. K should not make the loan. b.

If coverage ratio falls below 4, expected payoff is: 0.95 × 40 + 0.04 × 0 + 0.01 × -500 = 38 - 5 = $33.

If coverage ratio does not fall below 4, expected payoff is: 0.85 × 40 + 0.14 × 0 + 0.01 × -500 = 34 - 5 = $29. Since the probability of the coverage ratio falling below 4 is 0.60, the unconditional expected rate of return is:

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(0.6 × 33 + 0.4 × 29)/500 = (19.8 + 11.6)/500 = 31.4/500 = 0.0628 Since this is greater than 6%, Mr. K should make the loan.

17.

The payoff table is: a1 (8% interest)

a2 (5% interest)

Payoff

Probability

Payoff

Probability

Bankrupt

-.80

0.05

-.80

0.01

Not Bankrupt

.08

0.95

.05

0.99

Payoffs are in terms of rate of return for consistency with Toni’s mean-variance utility function. For example, if Tech goes bankrupt, (net) return is

2,000 − 10,000 = −.80 10,000 a.

First, we calculate the expected rates of return and variances of return for

each act: xa1 = 0.05 (-.80) + 0.95 (.08) = -.04 + .076 = .036

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xa2 = 0.01(-.80) + 0.99 (.05) = -.0080 + .0495 = .0415 σa1

2

2

2

= 0.05 (-.80 - .036) + 0.95 (.08 - .036) = .05 (.6989) + 0.95 (.0019) = .0349 + .0018 = .0367

σa2

2

2

= 0.01 (-.80 - .0415)

+

2

0.99 (.05 - .0415)

= 0.01 (.7081) + 0.99 (.0001) = .0071 + .0001 = .0072 Then: EU(a1) = 2 (.036) - .0367 = .0720 - .0367 = .0353 EU(a2) = 2 (.0415) - .0072 = .0830 - .0072 = .0758 Toni should take a2.

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It appears that the contract is incomplete, that is, no procedures are laid

down in the contract to deal with the effects of a change in GAAP on the covenant ratio. Therefore, due to contract rigidity, it will be hard to change the contract if GAAP changes. A change in GAAP that lowers reported net income and/or increases its volatility will then be of concern to the manager because the probability of violation of covenant ratios will increase. This will impose costs on the firm and its manager, especially if the manager’s compensation depends on reported net income and/or share price.

18.

The manager’s expected utility for a1 is:

[ = 0.6[0.5

]

[

]

EU (a1 ) = 0.6 0.5 .322 × 110 + 0.5 .322 × 90 + 0.4 0.5 .322 × 55 + 0.5 .322 × 45 − 2

]

[

]

35.42 + 0.5 28.98 + 0.4 0.5 17.71 + 0.5 14.49 − 2

= 0.6 × 5.66 + 0.4 × 4.00 − 2 = 3.40 + 1.60 − 2 = 3.00

Expected utility for a2 is: EU (a 2 ) = 0.4 × 5.66 + 0.6 × 4.00 − 1.7 = 2.26 + 2.40 − 1.7 = 2.96

The manager will work hard (a1) and receive reservation utility of 3. The contract of Example 9.4 is more efficient than the contract of Example 9.3 because the manager attains reservation utility with a lower profit share. That is, the manager bears less compensation risk. This greater efficiency is evidenced

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by an increase in the owner’s expected utility from 53.92 in Example 9.3 to 54.24 in Example 9.4. The agency cost is reduced by .32. Accountants can increase contracting efficiency by reducing the noise in net income, that is, by improving the ability of net income to predict the payoff. This can be accomplished by improved measurement. Examples include better estimates of environmental liabilities and of the value of R&D.

19.

a.

Three (pure strategy) Nash equilibria are (Violate, Keep), (Keep, Violate)

and (Violate, Violate), where the first word within brackets denotes country 2's strategy. b.

Country 1 could switch to Violate, thereby punishing country 2 for not

playing Keep. When the game is repeated, each of the players realizes that it is to their mutual benefit to play (Keep, Keep). This is because each country will perceive that if it violates, the other country can punish it by switching to violate at the next opportunity, that is in the next period. Thus, both countries seem to have an incentive to play (Keep, Keep). But, this reasoning breaks down in the last period. At the beginning of the last period, both players realize that it will not be possible for the other party to punish a switch to violate. Thus they both have an incentive to switch strategies in the last period, in which case the payoff is (50, 50). Now, consider the second-last period. Knowing what will happen in the last period, each player will realize that it will not be possible for the other party to punish violation taking place in the second-last period, since both will be violating in the last period anyway. Thus, each party has an incentive to switch to violate in the second-last period. This reasoning works backwards each period to the current one. Any attempt at cooperation unravels and the predicted strategy pair is (Violate, Violate) in each

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period. Note that an inability to enter into binding agreements is crucial to this argument. c.

If the game is repeated indefinitely, the above unravelling argument

breaks down, since there is no last period. Then, a likely outcome of the game, even though it is non-cooperative, is the strategy pair (Keep, Keep).

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Additional Problems 9A-1. The instability of economic cartels such as OPEC (Organization of Petroleum Exporting Countries) can be explained, at least in part, by game theory considerations. Typically such cartels attempt to agree to restrict oil production and keep prices to customers high. Frequently, however, some countries violate these agreements. Required Use the following depiction of a two-country non-cooperative game to explain why violation occurs. That is, explain in words which strategy pair is likely to be played in this game and why. Identify the Nash equilibrium of this game.

Country 1 Keep

Violate

Keep

100, 100

40, 200

Violate

200, 40

50, 50

Country 2

In each box, the first number represents country 2’s payoff and the second country 1’s payoff.

(CGA-Canada)

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9A-2. A manufacturer of farm equipment is headed for financial distress. Bonuses of management are based on net income relative to budget. There has been a recent change in management, occurring in early 2001. To the surprise of the new manager, the outgoing manager had sharply increased 2000 production, resulting in excessive levels of inventory on hand at the end of 2000. The manufacturer uses absorption costing for its inventories. Required a.

Explain why the old management increased production and inventories.

b.

How might the remuneration plan of management be changed to reduce

the likelihood that this would happen in the future? (CGA-Canada) 9A-3. Suppose there is a company with a number of divisions that are profit centres, all sharing a common production facility (for example, a machine shop). The user divisions are always submitting rush orders to the operator of the common production facility. The division involved (division A) claims the order is urgent and that delay will result in significant profit losses to the company, a claim that is very difficult for the operator of the common facility to verify or refute. What sometimes results is a job being given priority, which causes a delay of some other division’s job, where the cost of delay to the company (forgone profits due to, say, impatient customers going elsewhere) is well in excess of the cost of delay to division A. Assume that each division manager receives a bonus based solely on the profits of his or her division, in addition to fixed salary. Required a.

Explain why the behaviour of division A’s manager is predictable, in terms

of agency theory. b.

Can you think of a solution to this agency problem? Explain why your

solution works.

(CGA-Canada)

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9A-4. The shareholders of UVW Ltd. are unhappy about the top manager’s performance. While the manager’s effort in running the firm cannot be observed, it is felt that he or she puts in effort amounting to about 40 hours a week. The manager’s annual salary at present is $160,000.

A new incentive contract is being considered by the shareholders, whereby the manager would receive a salary of $100,000 per annum plus a bonus of 25% of reported net income before salary and bonus.

You are asked to analyze the expected impact of the new bonus plan on the manager. You estimate that if the manager puts in about 60 hours per week (a1), net income before manager remuneration will be $1,040,000 per annum with probability of 0.7, and $90,000 per year with probability of 0.3. Under the present salary-based remuneration, whereby the manager’s effort is 40 hours per week (a2), analysis of past profitability shows that annual net income has been $1,040,000 with probability of only 0.1 and $90,000 with probability of 0.9.

You also ascertain that the manager’s utility for money is equal to the square root of the money received, and that disutility for effort is four times the number of hours worked per week. Required a.

Show calculations to verify that under the present salary-based

remuneration plan the manager will prefer to work 40 hours per week over 60 hours. b.

Which act, a1 or a2, will the manager prefer under the new incentive

contract? Show calculations.

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A new accounting standard is proposed that, while it will not change future

expected net income, will greatly increase the volatility (i.e., reduce the precision) of net income. Explain why the manager would object to the proposed new standard.

9A-5. One of the problems of entering into contracts, including executive compensation contracts, is incompleteness. That is, it is generally impossible to foresee all relevant events that might happen and build provisions for them into the contract. An example of contract rigidity in the face of an unforeseen event appeared in the Wall Street Journal (April 15, 1993) in an article entitled “Firms Get Around Big One-Time Earnings Hits to Save Executive Bonuses.”

The article discusses SFAS 106, which requires that firms accrue employees’ OPEBs benefits, rather than waiting until they are paid (see Section 7.2.6). The article states that because of SFAS 106 “many compensation committees want to use operating earnings—not net after the accounting change—to calculate top managers’ bonuses.”

For example, Chrysler Corp., which had a charge for retiree health costs of $4.7 billion in 1993, plans to ask its shareholders if it could exclude the charge to calculate bonuses. However, there is opposition by the United Shareholders Association, who believe that charges such as postretirement benefits “should be deemed a regular business cost, not an unusual expense to be ignored by board compensation committees.” However, consulting firm Wyatt Co. “says it’s simpler to exclude the new annual charges than to alter bonus formulas.” Required a.

If you were a Chrysler shareholder, would you agree to this request?

Explain why or why not. b.

If you were a senior Chrysler executive affected by SFAS 106 and your

request was turned down, how would you react? Explain why.

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9A-6. Mr. Kao, the owner of Kao Industries, wants to hire a manager to operate the firm while he takes an extended trip abroad. He wants the manager to work hard (60 hours per week) rather than shirk (40 hours per week). The payoff table for Kao Industries under each alternative is as follows: Kao Industries Payoff Table for Year NET INCOME FOR YEAR

PROBABILITY

PROBABILITY

(a1 = 560 hours)

(a2 = 540 hours)

$400

0.7

0.2

200

0.2

0.3

0

0.1

0.5

(before manager remuneration)

Mr. Kao is negotiating with a potential manager about the remuneration contract. The manager’s disutility for effort for the year is:

h2 Disutility of effort = 800 where h is the number of hours worked per week. Required a.

Show calculations to verify that for a fixed annual salary paid to the

manager, Mr. Kao will prefer that the manager work hard. Mr. Kao is risk-neutral. b.

For any fixed annual salary, will the manager prefer to work hard or to

shirk? Explain.

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Suppose that Mr. Kao offers the manager a fixed annual salary of $10,

plus 10% of net income. The manager’s utility for money is equal to the square root of the money received. Assuming that the manager takes the job, which act would he or she take? Show your calculations. (CGA-Canada)

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9A-7. Non-cooperative game theory is a way of modelling the conflict situation that exists between a firm manager and investors. Consider the following depiction of a game between a manager/entrepreneur and a potential investor in the firm.

Manager/Entrepreneur Work hard

Shirk

Invest

7, 6

2, 7

Do not invest

5, 3

6, 5

Investor

The manager may choose to work hard or shirk. The number pairs show the payoffs to the investor (first number) and the manager (second number) for each manager/investor strategy pair. For example, if the investor invests and the manager works hard, they receive payoffs of 7 and 6 respectively. Required a.

Identify the cooperative solution and explain why it is not a Nash

equilibrium. b.

Identify a Nash equilibrium and explain why it is the predicted outcome of

a single play of the game.

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Suggested Solutions to Additional Problems 9A-1. The payoff table for the two-country, non-cooperative game, repeated here for convenience, is:

Country 1

Country 2

Keep

Violate

Keep

100, 100

40, 200

Violate

200, 40

50, 50

The first number in each box represents country 2's payoff. To see why violation of the keep/keep agreement may occur, we see that if country 2 keeps but country 1 violates, country 1 receives a payoff of $200. Thus, country 1 has an incentive to violate the keep/keep agreement. Similar reasoning applies to country 1. However, if one or more countries violate, the cartel agreement has broken down, other countries will also violate, and each country ends up with $50. The (50, 50) payoff is the Nash equilibrium of the game. While both countries would be better off if they both played a keep strategy, by doing so, each country is tempted to violate the cartel agreement. If they both violate it, they end up at (50, 50).

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It appears that the old management increased production and inventories

in order to maximize its bonus. This is because, under absorption costing, an increase in inventories will absorb overhead costs that would otherwise be charged against the current year’s net income. Given that the firm is headed for financial distress, increasing production and inventories may have been a way to report sufficient profits that the old management would receive a bonus. b.

Management should be given a longer-run perspective in operating the

firm than is created by basing bonus on reported net income for the year. A way to do this would be to base management compensation, at least in part, on share price performance. Management would realize that operating policies that increase current profits at the expense of future profits would not be in its own interests, since share price would respond negatively as soon as the production increase and resulting increase in inventories became known. Note that for this argument to hold, management must be required to hold shares received as compensation, possibly even beyond retirement or replacement. An alternative would be to base the bonus on longer-run net income, such as a 3 or 5-year average. It is unlikely that a policy such as manufacturing for stock could be sustained this long, since the inventory would have to be financed. Consequently, the likelihood that management would again unduly increase production is reduced.

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The company’s divisionalized form of organization, together with bonuses

paid based on divisional profits, creates a conflict situation between division managers. In agency theory, each manager is assumed to maximize his or her own expected utility. Consequently, division managers compete with one another for rush orders, regardless of the effect on overall company profits. b.

A solution would be to base bonuses at least in part on overall company

profit. Then, division managers know that their bonuses will suffer if they attempt to push through a rush order for their own division that results in sufficiently higher costs to another division that overall company profit is reduced. A possible disadvantage of this solution would arise if (as is likely) overall company profit is less correlated with the effort of a division manager than is divisional profit. Then, the incentive effect (i.e., the sensitivity) of the compensation contract is lower. The firm would have to increase incentive by loading more risk onto the division managers, for example by lowering salary and raising profit share, holding expected compensation constant. For risk-averse managers, this would lower their expected utility of compensation, so that their expected compensation would have to be raised to enable them to attain their reservation utility. This solution works if the increased expected manager compensation is less than the order delay costs to the company under the old contract. Note: It is assumed implicitly above that each manager knows only his or her own effort. It may be, however, that division managers may have information about the effort levels of other division managers as well. Then, the principal can design a more efficient incentive contract, based on overall company profit, that exploits this joint effort knowledge. See the discussion of the paper of Arya, Fellingham, and Glover (1997) in Section 10.2. However, the assumption of Arya, Fellingham and Glover that each division manager knows the effort of the others can be questioned in our context, since divisional contributions to overall firm profit can be difficult to assess objectively.

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Page

For an interesting article which questions the rewarding of managers and employees on the basis of firm-wide performance, see “Just desserts,” The Economist (January 20, 1994), p.71.

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If the manager works 60 hours per week (a1), his/her expected utility is: EU(a1) = 160,000 − 60 × 4 = 400 - 240 =160

If the manager works 40 hours per week (a2), his/her expected utility is: EU(a2) = 160,000 − 40 × 4 = 400 -160 = 240 Therefore, the manager will prefer to work 40 hours per week. b.

Under the new plan, the manager’s expected utility for a1 is: EU

new

( a 1 ) = 0 . 7 100 , 000 + 1, 040 , 000 × . 25 + 0 . 3 100 , 000 + 90 , 000 × . 25 − 60 × 4

= 0.7 × 600 + 0.3 × 350 - 240 = 285 Under the new plan, the manager’s expected utility for a2 is: EU new (a2 ) = 0.1 100,000 + .25 × 1,040,000 + 0.9 100,000 + .25 × 90,000 − 40 × 4

= 0.1 × 600 + 0.9 × 350 – 160 = 215 The manager will prefer to work 60 hours per week under the new plan.

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Since the manager is risk averse, an increase in the volatility of expected

future bonuses will decrease expected utility, holding the expected value of bonuses constant. Given contract rigidity, the manager will object to the new standard because the expected utility of remuneration is lower.

9A-5. a.

If the request is granted, a shareholder would realize that this would result

in a higher bonus to managers, given the bonus formula. As a result, the shareholder may disagree with excluding the charge, particularly if he/she, like the United Shareholders Association, felt it was a valid business expense. This would be especially the case if the shareholder felt that the manager was already well-paid. Then, the bonus contract would be rigid, or resistant to change. A counter argument is that, according to agency theory, the lower manager compensation, if the charge is included, may cause the manager’s expected utility to fall below its reservation level. Then, the manager may leave the firm. To avoid this, the shareholder may agree to exclude the charge. Another argument against including the charge is that the manager may bias or manipulate reported earnings to make up for the shortfall. b.

Agency theory would predict the following reactions by an affected

manager: •

The initial reaction would be an increase in manager effort. For a

risk averse manager, a lower bonus as a result of the charge for postretirement benefits would raise the expected marginal utility of compensation. Then, since a rational, effort-averse manager will choose effort level so as to equate the expected marginal utility of compensation with the marginal disutility of effort, effort will rise to restore the manager’s equilibrium. In less technical terms, the manager will work harder so as to make up some of the lost compensation.

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A combination of lower expected utility of compensation and

greater effort could lower the manager’s expected utility below its reservation level. Indeed, it would do so, since the agency models of this chapter assume that the manager receives exactly his/her reservation utility. Then, the manager may leave the firm, or request a higher share of earnings for bonus purposes. •

The manager may react against the new accounting policy. This

could result in lobbying to have the new standard repealed or amended and/or in biasing (i.e., managing) reported net income so as to counter the effects of the standard on reported profits.

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Let the fixed annual salary be $w. Then, if hours worked are: •

a1 (60 hours per week): Mr. Kao’s expected payoff is: 400 × 0.7 + 200 × 0.2 + 0 × 0.1 - w = 320 - w

•

a2 (40 hours per week): Mr. Kao’s expected payoff is: 400 × 0.2 + 200 × 0.3 + 0 × 0.5 - w = 140 - w

Since his expected payoff is higher for any fixed w, Mr. Kao will prefer that the manager take a1. b.

The manager will prefer to shirk with a fixed annual salary. This is because

the same remuneration is received regardless of the act taken but the disutility of shirking (402/800) is less than that for working hard (602/800). c.

If the manager works hard (a1), expected utility EU of the manager is: EU(a1) = 0.7 U(10 + 40) + 0.2 U(10 +20) + 0.1 U(10) - 602/800

= 0.7 × 50 + 0.2 × 30 + 0.3 × 10 − 3,600 / 800 = 4.95 + 1.10 + .32 - 4.50 = 1.87 If the manager shirks (a2), expected utility of the manager is:

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EU(a2) = 0.2 × 50 + 0.3 × 30 + 0.5 × 10 − 1,600 / 800 = 1.41 + 1.64 + 1.58 – 2.00 = 2.63 Therefore, the manager will still prefer to shirk. The manager’s disutility for effort is sufficiently great that it outweighs the higher expected compensation under a1. Note: In questions such as this that involve the calculation of expected utility when utility of money is non-linear, students often tend to calculate the utility of the expectation rather than the expectation of the utility. For example, in the first part of c, many students calculate the expected compensation ($42) first, then take the square root, giving EU of 6.48 - 4.50 = 1.98, which is incorrect for a risk averse decision maker. Even though I warn them in advance, students will often make this error.

9A-7. a.

The cooperative solution is (invest, work hard). This is not a Nash

equilibrium, however. Since it is assumed that the parties do not agree to cooperate, the manager will change his/her action to shirk, thereby receiving a payoff of 7 rather than 6. The definition of a Nash equilibrium is that neither player has an incentive to change his/her action, given the action of the other player. Thus the cooperative solution does not meet the definition of a Nash equilibrium. b.

The Nash equilibrium solution is (do not invest, shirk). If the investor

invests, the manager’s highest payoff is given by shirking. If the manager shirks, the investor’s highest payoff is given by not investing. Thus, without an agreement to cooperate, neither player has an incentive to change his/her act given the act of the other player. This is the definition of a Nash equilibrium.

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