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Game Theory

Game Theory. Mike Shor Lecture 10. “A little knowledge is a dangerous thing. So is a lot.”. - Albert Einstein. Incentive Schemes. Salary and bonus contracts can compensate for information asymmetry Often, this is unreasonable

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Game Theory

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

  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

  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 • What is the chance that you have the disease if you tested positive?

  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 year • Reduce this year’s growth • Output / Quantity • Reduce quality • Average customer satisfaction • Reduce number of service calls

  7. Strategic Considerations • If bonus is tied to … • Market share • Firm profits • Industry profits

  8. 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) = -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

  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)

  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: $1.7M low quality worker: $1.4M • Disutility per MBA class high quality worker: $5,000 low quality worker: $10,000

  27. “High” Quality Workers • If I get an MBA: • Signal I am a high quality worker • Receive $1,700,000 - $5,000 N • If I don’t get an MBA • Signal I am a low quality worker • Receive $1,400,000 1,700,000 – 5,000 N > 1,400,000 300,000 > 5,000 N 60 classes > N

  28. “Low” Quality Workers • If I get an MBA: • Signal I am a high quality worker • Receive $1,700,000 - $10,000 N • If I don’t get an MBA • Signal I am a low quality worker • Receive $1,400,000 1,700,000 – 10,000 N < 1,400,000 300,000 < 10,000 N 30 classes < 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)

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