INFORMATION

1. INFORMATION © 2004 NYU Stern

2. Overview • Context: You want to reward good performance by a subordinate, but he has a better idea what that performance is than you do. What should you do? • Concepts: principals and agents, incentives, asymmetric information, adverse selection, moral hazard, signaling, reputation. • Economic principle: when people have superior information, expect them to use it to their advantage.

3. Typical scenarios • Agency problem: a principal (e.g., employer) wants to contract with an agent, but the former cannot observe the latter’s actions (moral hazard). • Lemons problem (or adverse selection). One party (e.g., car seller) has better information than the other. • Signalling problem. A player chooses its actions strategically so as to influence others’ beliefs (e.g., reputation).

4. Agency • Terminology: We refer to the payer as the principal, the payee as the agent, and the analysis as principal-agent or agency theory. • S. Kerr, “On the folly or rewarding A, while hoping for B.” • Performance is hard to measure. Any measurement system can be gamed. • Incentives work. Expect to get exactly what you pay for.

5. Agency examples • Sears in California paid auto mechanics based on the number of things they fixed. • Stock options as executive compensation. Why not to use industry-linked or indexed options? • Auditing firms are paid by the firms they audit. Moreover, they often make far more from consulting relationships than auditing. • Regulation. Telephone rates must be approved by state regulators. The latter try to reconcile the social benefits of marginal cost pricing with the need for firms to make a reasonable rate of return.

6. Managerial incentives How should shareholders reward managers? • Firm performance depends on manager’s action: • Action A implies $20m profits with probability 80%, $10m profits with probability 20%. • Action B implies $20m profits with probability 10%, $10m profits with probability 90%. • Shareholders cannot observe manager’s action, only firm performance. • Personal cost to manager of taking action A is $50k. • Manager’s “outside option” is to earn $200k.

7. Managerial incentives… • Plan 1: fixed salary. • Binding constraint is the “participation constraint:” must offer $200k, otherwise manager will leave. • Manager only cares about her salary, thus she will choose action B. • Firm’s expected profit = 10% 20 + 90% 10 = $11m.

8. Managerial incentives… • Plan 2: a% share in profits. • If manager chooses A, expected payoff is a%*(80%*20m+20%*10m)-50k = a%*18m-50k • If manager chooses B, expected payoff is a%*(10%*20m+90%*10m) = a%*11m • If shareholders want to induce manager to choose action A, a must be at least .714%. • But a = .714% would lead to an expected payoff of 0.714%*18m-50k = 78.5k, which is less than 200k.

9. Managerial incentives… • Plan 2 (cont) • Should set a such that a%*18m-50k is at least 200. Result: a = 1.38%. • Firm’s expected profit = 80% 20 + 20% 10 = $18m. • Even taking away 1.38% for manager, this is still more than $11m. • Problem: manager is taking on a high-risk gamble. With 20% probability, her payoff is only 1.38%*10m-50k = 88k.

10. Managerial incentives… • Plan 3 (the best): combination of fixed salary w and profit share a. • Set a = .714%. This should be enough to induce manager to choose action A. • Set w = 200 – (.714%*18m–50k) = 121,5k. This implies, by construction, that manager’s expected payoff is 200k. • Firm receives the same expected profit as under Plan 2, but manager is now guaranteed a minimum payoff of 121.5 + .714%*10m – 50k = $142.9k.

11. Typical scenarios • Agency problem: a principal (e.g., employer) wants to contract with an agent, but the former cannot observe the latter’s actions (moral hazard). • Lemons problem (or adverse selection). One party (e.g., car seller) has better information than the other. • Signalling problem. A player chooses its actions strategically so as to influence others’ beliefs (e.g., reputation).

12. The “lemons” problem • When the uninformed player moves first, she must think about how informed players will use their information: • Examples: product quality, insurance, credit. • General result: Tendency for low-quality products (or high-risk customers) to flood the market. • Solutions: warranties, reputation and branding, credit rationing, verification (medical examinations).

13. Please accept my resignation. I don't care to belong to any club that will have me as a member. -- Groucho Marx

14. Life insurance • How should you price life insurance if buyers know their risk but you do not? • If you charge a price low enough to appeal to low risk customers, who will buy? • If you raise the price, who will buy? • What price should you charge?

15. Winner’s curse • Common value auction: the object is worth the same for every bidder, each bidder gets an unbiased signal of value. • Examples: oil field, penny jar. • Expected valuation given signal: unconditional and conditional on being the highest bid. • Optimal strategy is to bid much less than signal estimate. Discount should be greater the greater the number of bidders or the closer to common value is the auction.

16. Games with uncertainty • Consider an additional, non-strategic player: Nature. • If a certain variable can take several values, let Nature “decide” which value it will be (according to the underlying probabilities). • Asymmetric information: a player who moves before Nature does not know the value. A player who moves after Nature and observes Nature’s move, knows the value.

17. Chocolate wars revisited • Publicity from the product placement increases Mars‘s profits by $800,000, decreases Hershey’s by $100,000. • Hershey's increase in market share costs Mars $500,000. • Benefit to Hershey from having its brand featured is given by b. • Hershey knows the value of b. Mars knows only that b=$1,200,000 or b=$700,000 with equal probability.

18. Chocolate wars [-200, -100] buy buy [-500, 200] [-500, 200] M H b = 1200 (50%) [0, 0] not buy not buy N [-250, 100] buy [-500, -300] [0, 0] b = 700 (50%) H not buy [0, 0]

19. Typical scenarios • Agency problem: a principal (e.g., employer) wants to contract with an agent, but the former cannot observe the latter’s actions (moral hazard). • Lemons problem (or adverse selection). One party (e.g., car seller) has better information than the other. • Signalling problem. A player chooses its actions strategically so as to influence others’ beliefs (e.g., reputation).

20. Signaling • When the informed player moves first, she must think about the information conveyed by her actions to uninformed players (the “signal”): • Does a low price suggest low quality? • Advertising as a signal. • Job market signalling. • Incumbent firm’s reaction to entry.

21. Price as a signal of quality • One seller of stereo equipment, many buyers. Seller sets price, buyers decide whether or not to buy (one unit each max). Seller knows quality of stereo, buyers do not. • Demand • 80% of the customers are willing to pay at most $200 regardless of quality; • 20% of the customers would pay $400 for high-quality product, only $200 for low quality one. • Costs • High quality product costs $300; • Low quality product costs $100.

22. Price as a signal of quality… • Claim: It is an equilibrium for seller to set p=400 if quality is high and p=200 if quality is low. • In this equilibrium, price conveys information about quality: consumers know that a high price implies high quality. • Why wouldn’t a low-quality seller want to “masquerade” as a high-quality seller by setting a high price? Because it loses too much of the market. (Numbers are profit per customer.) p=400 Þ Profit = (400 - 100) x 20% = 60 p=200 Þ Profit = (200 - 100) x 100% = 100

23. Signaling equilibria • In the previous game, we have a separating equilibrium: different types of seller choose different strategies. • High quality seller chooses different strategy so as to ensure buyer knows she’s buying from a high quality seller. In order for this to work, it must be the case that imitation is very costly. • If imitation costs are not very high, we have a pooling equilibrium. In this case, the “bad” type imitates the good type so as to acquire a reputation for being good. • In a multi-period situation, pooling may become attractive: the cost of imitating early on pays off in terms of future payoffs: reputation building.

24. Reputation for toughness • Market has monopolist and potential entrant. • If no entry monopolist gets 4, entrant 0. • If entry and collusion/cooperation each get 1. • If entry and a fight each lose 1. • What is Nash equilibrium?

25. Reputation for toughness… • What if Monopolist faces a potential entrant in each of a series of local markets? (Cf American Tobacco example.) • By teaching entrant a lesson in first markets, Monopolist might be able to discourage entrants in other markets. • Key (gang-of-four): Assume that there is some chance monopolist is a “Rambo” monopolist whose payoff to cooperation is less than –1.

26. Reputation for toughness… • Entrants believe Monopolist is “tough” with probability a. • Suppose Monopolist fights entry even if it is not “tough”. • A second entrant still believes Monopolist is tough with probability a. Expected value from entry is a(–1) + (1-a)1. If a>1/2, entrant stays out. • For a normal Monopolist, fighting the first entrant is an investment in reputation. • (Advanced note: in this case, equilibrium would require mixed strategies, similar to bluffing in poker or serving in tennis.)

27. Takeaways • Think about how your rival will: • Use its information advantage; Or • React to your information advantage. • You will get what you reward. • Beware of the Groucho Marx problem: low-quality products or customers flood the market. (Or: If this is such a good deal, why are you offering it to me?) • Your actions convey information and create reputations.

28. Practice: Coke v Pepsi • You work for Pepsi. The company has just signed a major star endorsement. You must decide how much to spend on your Summer ad campaign. Net profits (in $m) depend on how much you and Coke spend – and on whether or not Coke has signed a major star: Coke’s adv 2 1 Coke’s adv 2 1 3 2 0 1 2 2 0 1 4 6 Pepsi’s adv Pepsi’s adv 5 3 4 2 1 1 2 3 1 2 (a) Coke signed major star (b) Coke did not

29. Coke v Pepsi… • Coke’s decision of whether to sign a major star has already been taken. You don’t know what the decision was. Your CIO tells you that there is a 70% chance they did. • You also know that Coke will have a chance to react to your decision of how much to spend. • Should you go for a $1m or a $2m campaign?

30. Coke v Pepsi intuition • This is a sequential game with incomplete information. Let us solve it backwards and include “Nature”. • If Coke did sign a star, then it will choose $2m if and only if Pepsi chooses $2m. If Coke did not sign a star, then it will choose $1m regardless of what Pepsi chooses. • Moving backwards: • If Pepsi chooses $1m, then Coke will choose $1m. Pepsi’s expected payoff is 70% 2 + 30% 3 = $2.3m. • If Pepsi chooses $2m, then Coke will choose $2m with probability 70%, $1m with probability 30%. Pepsi’s expected payoff is 70% 0 + 30% 6 = $1.8m. • Pepsi should choose $1m. (What considerations are we leaving out of the analysis?)

31. Coke v Pepsi game tree P 1 2 70% 0 + + 30% 6 = 1.8 70% 2 + + 30% 3 = 2.3 N N star (70%) no star (30%) star no star (30%) C C C C 1 2 1 2 1 2 1 2 1 4 2 2 0 3 4 0 2 5 3 3 1 2 6 1

32. Practice: credit cards • Most profitable customers are those who maintain large balances and don’t default. (Other profitable types: big spending customers – the Amex model.) • Idea: balance transfer at a reduced interest rate. To whom does this appeal? What would you expect to happen?

33. Practice: sale of Shearson • In the early 1990s, American Express held talks to discuss the sale of its Shearson brokerage unit to Primerica (a precursor of Citigroup). The deal made strategic sense for both companies. • The stumbling block was outstanding legal claims against Shearson: the value of these claims was hard to judge, and Primerica was in a poor position to judge them in any case. • How would this affect the negotiation? What solutions come to mind?

34. Practice: Sale of business The problem: • Seller’s value is between $100m and $200m, uniformly distributed. The seller knows this value, but the buyer only knows the distribution. • Buyer’s value is equal to seller’s value plus $10m (there are gains from trade). • Buyer must make take-it-or-leave-it offer of some price p. How much?

35. Sale of business unit… Suppose buyer offers p (in $m). • Probability seller will accept offer: (p-100)/100. • Buyer’s expected value in case offer is accepted: (100+p)/2+10. (Average of 100 and p, plus 10.) • Buyer’s expected payoff: (p-100)/100 [(100+p)/2+10-p]. • Maximize with respect to p: p=110.

36. Sale of business unit… Suppose buyer offers p=110 (in $m). • In most cases (90%) offer is rejected. • Offering more would imply higher probability of sale, but expected value of unit would increase by less than price paid. • Intuition = adverse selection: seller will only sell if unit’s is relatively low. Question: Why did American Express indemnify Primerica? Because not doing so would have led to a lower price.