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INFORMATION © 2004 NYU Stern 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?

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Information l.jpg

INFORMATION

© 2004 NYU Stern


Overview l.jpg
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.


Typical scenarios l.jpg
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).


Agency l.jpg
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.


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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.


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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.


Managerial incentives7 l.jpg
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.


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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.


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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.


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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.


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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).


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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).


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Please accept my resignation.

I don't care to belong to any club

that will have me as a member.

-- Groucho Marx


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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?


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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.


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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.


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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.


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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]


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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).


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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.


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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.


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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


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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.


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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?


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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.


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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.)


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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.


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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


Coke v pepsi l.jpg
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?


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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?)


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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


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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?


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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?


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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?


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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.


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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.


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