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

Mike Shor Game Theory & Business Strategy 2 Incentive Schemes Salary and bonus contracts can compensate for information asymmetry Often, this is unreasonable  Employees unwilling to assume risks  Contracts must be perfectly balanced  May be better to settle for low effort Today:  The flip side – are bonuses going to good employees or just lucky ones?  Signaling & screening

Mike Shor Game Theory & Business Strategy 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?

Mike Shor Game Theory & Business Strategy 4 Bayes Rule

Mike Shor Game Theory & Business Strategy 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.”

Mike Shor Game Theory & Business Strategy 6 Leakages If bonus is tied to  Increases over last year  Reduce this year’s growth  Output / Quantity  Reduce quality  Average customer satisfaction  Reduce number of service calls

Mike Shor Game Theory & Business Strategy 7 Strategic Considerations If bonus is tied to …  Market share  Firm profits  Industry profits

Example Pharmaceutical Development

Mike Shor Game Theory & Business Strategy 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.”

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 11 Market Conditions Independent labs contracted Average cost of labor: $16/hour Chance of success:  Minimally:1%  Maximally:2.5%

Mike Shor Game Theory & Business Strategy 12 Cost Calculations Extra cost to lab of high effort: 40 hours / week / employee x25 weeks time frame x $16 / hour _ = $16,000 / employee

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 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”

Mike Shor Game Theory & Business Strategy 15 Extra Profit if it Works Value of extra chance of success:  x $2B = $30M Cost of bonus:  x $75M = $2M Benefit of plan:  $30M – $2M = $28M

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 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!

Mike Shor Game Theory & Business Strategy 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!

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 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?

Mike Shor Game Theory & Business Strategy 21 Self-Selection High risk drivers:  Don’t buy insurance:(.9)(-10,000)= -9K  Buy insurance:= -5K  High risk drivers buy insurance Low-risk drivers:  Don’t buy insurance:(.1)(-10,000)= -1K  Buy insurance:= -5K  Low risk drivers do not buy insurance Only high risk drivers “self-select” into the contract to buy insurance

Mike Shor Game Theory & Business Strategy 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)= $9,000  Insurance company loss: $4,000 Cannot ignore this “adverse selection” If only going to have high risk drivers, might as well charge more ($9,000)

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 25 Screening Education as a signaling and screening device Is there value to education? Good types: less hardship cost

Mike Shor Game Theory & Business Strategy 26 Example: MBAs How long should an MBA program be? Two types of workers:  High and low quality  NPV of salary high quality worker:$1.6M low quality worker:$1.0M  Disutility per MBA class high quality worker:$5,000 low quality worker:$20,000

Mike Shor Game Theory & Business Strategy 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 > 5,000N 120> N

Mike Shor Game Theory & Business Strategy 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 < 20,000N 30< N

Mike Shor Game Theory & Business Strategy 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

Mike Shor Game Theory & Business Strategy 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!

Mike Shor Game Theory & Business Strategy 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)