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Analyzing Conflict Through Non-Cooperative Game Theory and Agency Models

This chapter provides an in-depth analysis of conflict using the principles of non-cooperative game theory and agency theory. It covers utility payoffs in non-cooperative games, Nash equilibrium, and the moral hazard problem of information asymmetry within agency contracts. The discussion includes real-world examples where agents, such as managers and professionals, are incentivized to work hard despite risk aversion and the challenges of monitoring their efforts. Insights into cooperative solutions and the implications of reputation in managerial decision-making are also highlighted.

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Analyzing Conflict Through Non-Cooperative Game Theory and Agency Models

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  1. Chapter 9 An Analysis of Conflict

  2. Chapter 9An Analysis of Conflict

  3. 9.3 A Non-Cooperative Game Table 9.1 UTILITY PAYOFFS IN A NON-COOPERATIVE GAME Manager HONEST (H) DISTORT (D) BUY (B) 60, 40 20, 80 Investor REFUSE TO BUY (R) 35, 20 35, 30 • Continued

  4. 9.3 A Non-Cooperative Game (continued) • Nash equilibrium solution • RD: payoffs 35,30 • Cooperative solution • BH: payoffs 60, 40 • Single play of the game • Why is BH unlikely? • Multiple plays: BH more likely • Manager reputation and ethical behaviour • Folk theorem

  5. 9.4 Agency Theory • A principal wants to hire an agent for some specialized task • Assume single-period, for simplicity • Agency models separation of ownership and control • Principal and agent are rational. Agent is risk-averse. Principal may be risk-averse, but assume risk-neutral for simplicity • Principal wants agent to work hard, but • Agent is effort-averse

  6. Moral Hazard Problem of Information Asymmetry • Principal cannot observe manager effort - call it a • Call manager’s disutility of effort V(a) • More effort ---> greater disutility • Implies manager may shirk on effort • E.g., if paid a fixed salary, how hard will the manager work? • Analogy: if no final exam, how hard will students work?

  7. Examples of Agency Contracts • What gives the following agents an incentive to “work hard” for the principal? • Doctor, dentist • Lawyer • Auditor • Hockey player • Construction worker • Manager

  8. 9.4.2 Agency Contract Example • Owner: rational, risk-neutral • Wants manager to work hard, to max. expected firm payoff x • Think of x as the total cash flow to be realized from manager’s current-period effort • Manager: rational, risk-averse and effort-averse • Wants to max. expected utility of compensation c, net of disutility of effort V(a) • If manager works hard, V(a) = 2 units of disutility • If manager shirks, V(a) = 1.71 • Continued

  9. 9.4.2 Agency Contract Example (continued) • Motivating the manager to work hard • Salary: manager will shirk • Direct monitoring of manager effort: unlikely in owner/manager context. Manager will shirk • Indirect monitoring: Unlikely in owner/manager context unless moving support. Manager will shirk • Owner rents firm to manager: Manager will work hard, but manager bears all the risk, requires low rent for manager to attain reservation utility • Give manager a share of the payoff • Continued

  10. 9.4.2 Agency Contract Example (continued) • A problem arises if manager paid a share of payoff • Firm payoff x not known until after contract expires (single period contract). • Some manager effort does not pay of in current period • e.g., R&D, contingencies • Manager has to be paid at contract expiry • A solution • Base manager compensation on a performance measure (e.g., net income), which is available at period end • Continued

  11. 9.4.2 Agency Contract Example (continued) • To motivate manager effort, most efficient contract may base manager compensation on a share of firm net income • Will manager be willing to accept contract? • Concept of reservation utility, call it R • If manager is to work for owner, must receive expected utility of at least R • Level of R depends on manager reputation • R treated as fixed in a single-period contract • Continued

  12. 9.4.2 Agency Contract Example (continued)

  13. Example 9.3 Agency Contract • Assumptions • Manager has 2 effort choices: • Work hard (a1 ) • Shirk (a2 ) • If manager works hard x = 100 with prob. 0.6 x = 55 with prob. 0.4 • If manager shirks x = 100 with prob. 0.4 x = 55 with prob. 0.6 Note fixed support • Continued

  14. Example 9.3 Agency Contract (continued) • Assumptions, cont’d • Manager’s contract (linear): c = ky, 0 ≤ k ≤ 1 • y is net income • k is manager’s share of net income • Manager’s reservation utility: R = 3 • Quality of net income y (noisy, but unbiased, e.g., fair value accounting) • If x is going to be $100 • y = $115 with prob. 0.8 • y = $40 with prob. 0.2 • If x is going to be $55 • y = $115 with prob. 0.2 • y = $40 with prob. 0.8 • Continued

  15. Example 9.3 Agency Contract (continued) • Manager’s utility EUm(a1) = 0.6[0.8(k × 115)1/2 + 0.2(k × 40)1/2] + 0.4[0.2(k × 115)1/2 + 0.8(k × 40)1/2] - 2 EUm(a2) = 0.4[0.8(k × 115)1/2 + 0.2(k × 40)1/2] + 0.6[0.2(k × 115)1/2 + 0.8(k × 40)1/2] – 1.71 • Owner’s utility (risk neutral) EUO(a1) = 0.6[0.8(100 - (1 – k) × 115) + 0.2(100 - (1 – k) ×40)] + 0.4[0.2(55 - (1 – k) ×115) + 0.8(55 - (1 – k) × 40)] • Continued

  16. Example 9.3 Agency Contract (continued) • Formal Statement of the Owner’s Problem • Find k to maximize EUO(a) Subject to: • Manager wants to take a1 (incentive compatibility—i.e., manager utility higher for a1 than a2) • manager receives reservation utility of R = 3 • The result: K = .3237 • Continued

  17. Example 9.3 Agency Contract (continued) • Check • Manager’s utility EUm(a1) = 0.6[0.8(.3237 × 115)1/2 + 0.2(.3237 × 40)1/2] + 0.4[0.2(.3237 × 115)1/2 + 0.8(.3237 × 40)1/2] – 2 = 3 EUm(a2) = 0.4[0.8(.3237 × 115)1/2 + 0.2(.3237 × 40)1/2] + 0.6[0.2(.3237 × 115)1/2 + 0.8(.3237 × 40)1/2] – 1.71 = 2.9896 • Manager wants to “work hard” since his/her utility is higher • Continued

  18. Example 9.3 Agency Contract (continued) • Check, cont’d. • Owner’s utility EUO(a1) = 0.6[0.8(100 - .3237 × 115) + 0.2(100 - .3237 ×40)] + 0.4[0.2(55 - .3237 ×115) + 0.8(55 - .3237 × 40)] = 55.4566 Compare with owner’s utility of rental contract (Example 9.2) = 51 Contract based on net income is more efficient

  19. Example 9.4 A More Efficient Contract • Retain Example 9.3 assumptions, except • Higher quality of net income y (less noisy, still unbiased) • If x is going to be 100 • y = $110 with prob. 0.8462 • y = $45 with prob. 0.1538 • If x is going to be 55 • y = $110 with prob. 0.1538 • y = $45 with prob. 0.8462 • Continued

  20. Example 9.4 A More Efficient Contract (continued) • Then k = .3185 (compared with .3237 in previous contract) EUm(a1) = 0.6[0.8462(.3185 × 110)1/2 + 0.1538(.3185 × 45)1/2] + 0.4[0.1538(.3185 × 110)1/2 + 0.8462(.3185 × 45)1/2] – 2 = 3 EUO(a1) = 0.6[.8462(100 – (.3185 × 110) + 0.1538(100 - .3185 ×45)] + 0.4[.1538(55 – (.3185 ×110) + 0.8462(55 - .3185 × 45)] = 55.8829 Compare with owner’s utility of 55.4566 in Example 9.3 Less noisy net income increases contract efficiency

  21. 9.5 Manager’s Information Advantage • Post-decision information • Manager can observe unmanaged net income, but owner can’t • In a single-period contract, rational manager will shirk and report highest possible net income • Example 9.5: Owner utility falls to 50.8165 • Continued

  22. 9.5 Manager’s Information Advantage (continued) • The revelation principle • If high net income is realized, manager will report high net income • Raise manager’s compensation if low net income is realized to the point where same compensation is received whether net income is high or low • Then, if low net income is realized, manager is indifferent between reporting high or low net income • Assume if indifferent, manager will report low net income if low net income is realized • Result: manager reports truthfully • Continued

  23. 9.5 Manager’s Information Advantage (continued) • Example 9.5 • Manager continues to shirk • Owner’s utility remains at 50.8165 as per example 9.5 • But, manager reports truthfully • No adverse selection problem • Continued

  24. 9.5 Manager’s Information Advantage (continued) • Problems in applying revelation principle in a financial reporting context • Manager may be punished for reporting the truth • May be fired if low net income reported • Contract restrictions • If compensation is capped, manager is effectively punished for reporting net income higher than cap • Restrictions on ability to communicate • Reporting the truth may impose legal liability and reputation loss on manager and owner, effectively blocking honest communication • Continued

  25. 9.5 Manager’s Information Advantage (continued) • Result of these problems is that it may be more efficient to allow some upwards earnings management • But manager will then overdose on earnings management • i.e., back to example 9.5 • A solution: restrict earnings management through GAAP • Continued

  26. 9.5 Manager’s Information Advantage (continued) • Example 9.7 • Illustrates how GAAP can restrict earnings management to point where manager must work hard to attain reservation utility • Some earnings management remains, but under control • Owner’s utility now 55.4981, up from Examples 9.5 and 9.6 (50.8165)

  27. 9.8 Implications of Agency Theory For Financial Accounting • The agency relationship is a contract. Contracts are rigid • Implies accounting policy choice and changes to accounting policy matter • Manager will usually object to new accounting standards that: • Lower reported net income (why?) • Increase its volatility (why?) • Continued

  28. 9.8 Implications of Agency Theory For Financial Accounting(continued) • Net income must be jointly observable (i.e., by manager and owner) • Role for GAAP, audit

  29. 9.8.1 Holmström’s Agency Model • Basing manager’s compensation on 2 variables is better than on 1 variable, unless the 2 variables are perfectly correlated • Example 9.9 • Holmström’s model implies that net income is in competition with share price performance for “market share” in compensation contracts • Continued

  30. 9.8.1 Holmström’s Agency Model (continued) • To maintain market share in compensation contracts, net income must be informative about manager effort • To be informative, net income must have • Sensitivity • Precision • These 2 desirable qualities usually have to be traded off • Similar to, but not same as, tradeoff between relevance and reliability

  31. 9.8.2 Contract Incompleteness & Rigidity • Basic reasons why accounting policies can have economic consequences • Incompleteness • Contracts cannot anticipate all possible state realizations • e.g., New accounting standards may arise during contract term • Manager’s net-income-based compensation may be affected • Debt covenant ration may be affected • Rigidity • Once signed, contracts hard to change • Result: accounting policies matter since they can affect contracts

  32. 9.9 Reconciliation • Contract incompleteness and rigidity mean that accounting policies matter • This argument does not conflict with efficient securities market theory

  33. 9.10 Conclusions • Accounting policies (even without cash flow effects) can have economic consequences and securities markets can still be efficient • Role of net income in monitoring and motivating manager performance equally important as informing investors • Net income competes with share price as a performance measure • Some earnings management can be “good” if controlled by GAAP

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