Game Theory “A little knowledge is a dangerous thing. So is a lot” - Albert Einstein Mike Shor Lecture 10

Game Theory

“A little knowledge is a dangerous thing.

So is a lot”- Albert Einstein

Mike ShorLecture 10

Mike ShorGame Theory & Business Strategy

2

Incentive Schemes Salary and bonus contracts can

compensate for information asymmetry Often, this is unreasonable

Employees unwilling to assume risksContracts must be perfectly balancedMay be better to settle for low effort

Today: The flip side – are bonuses going to good

employees or just lucky ones? Signaling & screening


3

A Horrible Disease A new test has been invented for a

horrible, painful, terminal disease

The disease is rare One in a million people are infected

The test is accurate 95% correct, 5% false positive/negative

You test positive! How worried are you?


4

Bayes Rule


5

Leakages

IBM Variable Pay Bonus of 10% of annual earnings if

“annual objectives are met in key areas”

Internal Memo:

“ We observe, across divisions, performance in line with expectations through about March. Performance declines consistently in later months.”


6

Leakages If bonus is tied to

Increases over last yearReduce this year’s growth

Output / QuantityReduce quality

Average customer satisfactionReduce number of service calls


7

Strategic Considerations

If bonus is tied to …

Market share

Firm profits

Industry profits

Example

Pharmaceutical Development


9

Goal: Align Research Labs’ Incentives

“ Strong resource devotion to select projects marginally increases the chance of success, but when considering the potential profitability of the post-patent market, it is clear that proper incentive alignment is essential.”


10

Market Conditions

Patent races over high-profit pharmaceuticals worth up to $2 billion

Resource devotion ranges from twenty to sixty hours per employee, with staff of fifty per project (low level to high level)

Project time frame: 6 months


11

Market Conditions

Independent labs contracted Average cost of labor: $16/hour

Chance of success: Minimally: 1% Maximally: 2.5%


12

Cost Calculations

Extra cost to lab of high effort:

40 hours / week / employee

x 25 weeks time frame

x $16 / hour _

= $16,000 / employee


13

To entice high effort Costs:

$16,000 per employee in costs

Benefits: 1½% extra chance of success (2½% - 1%)

Incentive compatibility:

.015 x bonus > $16,000

bonus > $1.1M


14

To entice high effort

Bonus per employee must be greater than $1.1 million

Fifty employees, so total bonus must be greater than $55 million

Final conclusion $75 million bonus “to be safe”


15

Extra Profit if it Works

Value of extra chance of success: 0.015 x $2B = $30M

Cost of bonus: 0.025 x $75M = $2M

Benefit of plan: $30M – $2M = $28M


16

Problem Ignoring individual incentives

Analysis assuming that entire group works hard or does not

Quick & Dirty Check: If fifty people working hard increases chance of

success by 1.5%, each person, on average, increases chance by only 1.5%/50 = 0.03%

Each person earns a bonus of $75M/50 = $1.5M


17

Conclusion

A person’s value of extra time:

$1.5M x 0.03% = $450

A person’s cost of extra time:

$16,000

NOT EVEN CLOSE!


18

Signaling

Definition Using actions that other players would

interpret in a way that would favor you in the game play

Requires It is not in the best interest for people to

signal falsely Implies signaling must be costly!


19

Auto Insurance

Half of the population are high risk drivers and half are low risk drivers

High risk drivers: 90% chance of accident

Low risk drivers: 10% chance of accident

Accidents cost $10,000


20

Pooling

An insurance company can offer a single insurance contract

Expected cost of accidents:(½ .9 + ½ .1 )10,000 = $5,000

Offer $5,000 premium contract The company is trying to “pool”

high and low risk drivers Will it succeed?


21

Self-Selection High risk drivers:

Don’t buy insurance: (.9)(-10,000) = -9KBuy insurance: = -5KHigh risk drivers buy insurance

Low-risk drivers:Don’t buy insurance: (.1)(-10,000) = -1KBuy insurance: = -5KLow risk drivers do not buy insurance

Only high risk drivers “self-select” into the contract to buy insurance


22

Adverse Selection

Expected cost of accidents in population (½ .9 + ½ .1 )10,000 = $5,000

Expected cost of among the insured.9 (10,000) = $9,000Insurance company loss: $4,000

Cannot ignore this “adverse selection” If only going to have high risk drivers,

might as well charge more ($9,000)


23

Screening

Offer two contracts, so that the customers self-select

One contract offers full insurance with a premium of $9,000

Another contract offers a deductible, and a lower premium


24

How to Screen

Want to know an unobservable trait Identify an action that is more costly for

“bad” types than “good” types Ask the person (are you “good”?) But… attach a cost to the answer Cost

high enough so “bad” types don’t lie Low enough so “good” types don’t lie


25

Screening

Education as a signaling and screening device

Is there value to education?

Good types: less hardship cost


26

Example: MBAs How long should an MBA program be? Two types of workers:

High and low quality NPV of salary

high quality worker: $1.6Mlow quality worker: $1.0M

Disutility per MBA classhigh quality worker: $5,000low quality worker: $20,000


27

“High” Quality Workers If I get an MBA:

Signal I am a high quality worker Receive $1,600,000 - $5,000 N

If I don’t get an MBA Signal I am a low quality worker Receive $1,000,000

1,600,000 – 5,000 N > 1,000,000

600,000 > 5,000N

120 > N


28

“Low” Quality Workers If I get an MBA:

Signal I am a high quality worker Receive $1,600,000 - $20,000 N

If I don’t get an MBA Signal I am a low quality worker Receive $1,000,000

1,600,000 – 20,000 N < 1,000,000

600,000 < 20,000N

30 < N


29

Hiding from Signals

The opportunity to signal may prevent some types from hiding their characteristics

Examples: Financial disclosures GPA on résumé Taking classes pass / fail


30

Hiding from Signals Suppose students can take a course pass/fail or for a

letter grade.

An A student should signal her abilities by taking the course for a letter grade – separating herself from the population of B’s and C’s.

This leaves B’s and C’s taking the course pass/fail. Now, B students have incentive to take the course for a letter grade to separate from C’s.

Ultimately, only C students take the course pass/fail.

If employers are rational – will know how to read pass/fail grades. C students cannot hide!


31

Summary

Enticing high effort is hard work Leakages Global vs. individual incentives Rewarding the right people

Screening Identify unobservable cost differences Exploit them (carefully)

Documents

Game Theory “A little knowledge is a dangerous thing. So is a lot” - Albert Einstein Mike Shor Lecture 10