Game Theory

1. Game Theory Topic 7Information “I like work. It fascinates me. I can sit and look at it for hours.” - Jerome Klapka Jerome

2. The Simpsons on Incentive Pay “If you don't like your job, you don't strike. You just go in every day and do it really half-assed. That's the American way.”

3. The Simpsons on Incentive Pay “Behold, the greatest breakthrough in labor relations since the cat o' nine tails!”

4. 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 • Employee Perceptions • Leakages • Group Rewards

5. 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?

6. Bayes Rule • What is the chance that you have the disease if you tested positive?

7. 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.”

8. 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

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

10. Example Pharmaceutical Development

11. 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.”

12. 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

13. Market Conditions • Independent labs contracted • Average cost of labor: $16/hour • Chance of success: • Minimally: 1% • Maximally: 2.5%

14. Cost Calculations • Extra cost to lab of high effort: 40 hours / week / employee x 25 weeks time frame x $16 / hour _ = $16,000 / employee

15. 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

16. 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”

17. 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

18. 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

19. 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!

20. Summary • Enticing high effort is hard work • Leakages • Global vs. individual incentives • Rewarding the right people • But often worth it ifyou can do it right