Principles of Game Theory

1. Principles of Game Theory Lecture 15: Screening

2. Administrative • Homework due Saturday • Will post a couple more questions for Tuesday. • Quiz Sunday • Final exam 1 week from today (Yikes!) • Over everything, but fewer questions on pre-midterm material

3. Last time • Signaling: • Using actions that other players would interpret in a way that would favor you in the game play • When constructing signaling devices: • It is not in the best interest for people to signal falsely • Implies signaling must be costly! • Full Signaling Game example • Separating equilibrium • Pooling • Hybrid (semi-separating)

4. Adverse Selection & Moral Hazard • Two ways we often think about incomplete information settings: • Adverse Selection • Uncertain about which type your playing with • Like the signaling game from last time • Other examples? • “before the fact uncertainty” • Moral Hazard • Unobservable actions (at least not perfectly) after your action • “after the fact uncertainty” • Examples?

5. Adverse Selection 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

6. Insurance 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?

7. Self-Selection • High risk drivers: • E(Don’t buy insurance): (.9)(-10,000) = -9K • E(Buy insurance): = -5K • High risk drivers buy insurance • Low-risk drivers: • E(Don’t buy insurance): (.1)(-10,000) = -1K • E(Buy insurance): = -5K • Low risk drivers do not buy insurance • Only high risk drivers “self-select” into the contract to buy insurance

8. 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)

9. Screening • Insurance company (and low risk customers!) would like to have a signaling mechanism • Screening • The difference between signaling and screening is a point of view. • Same as signaling but it’s from the receiver’s (rather than the sender’s) point of view

10. How to Screen? Want to know an unobservabletrait? • Identify an action that is more costly for “bad” types than “good” types • Ask the person are you “good”? (via an action) • But… attach a differential cost to the answer • Cost • High enough so “bad” types don’t lie • Low enough so “good” types don’t lie

11. Screening • Auto Insurance company could offer two contracts, so that “the right” customers self-select • One contract offers full insurance with a premium of $9,000 • Another contract offers a deductible, and a lower premium

12. Screening • Education as a signaling and screening device • Value to education? • Hopefully but there can still exist a “market” for it even when students don’t learn anything. • Requires that “good” types have less hardship cost • Example: How long should an MBA program be? • Two types of workers: low and high quality • N number of courses they must take. • 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

13. Decision for “High” Types Rational “high” type asks: • 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 Get an MBA if: 1,700,000 – 5,000 N > 1,400,000 300,000 > 5,000 N Indifferent at N = 60 classes

14. Decision for “Low” Types Rational “low” type asks: • 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 Don’t get an MBA if: 1,700,000 – 10,000 N > 1,400,000 300,000 > 10,000 N Indifferent at 30 classes

15. Decision for the MBA Admin • If more than 60 classes, neither type attends • If less than 30 classes, both types would attend but then the signal is meaningless and wouldn’t have value • Between 30 and 60 classes a separating equilibrium exists.

16. 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 • Why would a school want to allow a student to take a class pass/fail? • Humanities Faculty complain: “Students taking pass/fail don’t work as hard! Ba humbug!” • Nice schools: ‘allows opportunity to expand horizons…’ • Smart but maybe not as nice schools: we can game students against each other…

17. Counter intuitive implications Suppose students have the choice of taking a course for a letter grade or pass/fail: • An A student knows her abilities and will want to signal to employers, separating herself from B, C, and D students • This leaves B/C/D students taking the course pass/fail. But now B students have an incentive to signal to employers that they’re better than C/D students and work harder and take it for a letter grade. • … • This leaves only D students taking the course pass/fail.

18. Moral Hazard • Adverse Selection: you don’t know which type of employee is walking into your office • Moral Hazard: you don’t know what the employee will do after they go back to their office

19. Moral Hazard What happens when we have unobservable effort? • Example: A project with uncertain outcome • Probability of success depends on employee’s effort • P(success) = 0.6 if effort is routine • P(success) = 0.8 if effort is high • Employee has cost of effort • cost of routine effort = $100,000 • cost of high effort = $150,000 • Project outcome = $600,000 if successful

20. Compensation Schemes • How do you pay the employee? • Standard Benchmarks: • Fixed Salary • Observable Effort

21. Compensation Schemes • Scheme 1: Fixed Salary: • If employee puts in routine effort: • Utility = Payment - $100,000 • If employee puts in high effort: • Utility = Payment - $150,000  Employee puts in low effort! • Optimal Payment: lowest possible. • Payment = $100,000 • Value of project = (.6)600,000 = $360,000 • Expected Profit = $360 - $100 = $260K

22. Compensation Schemes • If effort is easy to observe, contracts are simple: • Work as hard as we tell you or get fired. • Only question is how hard do we want employees to work? • Salary must be commensurate with level of effort, or no one will take the job

23. Compensation Schemes • Scheme 2: Observable effort • Employee puts in effort level promised, given it’s pay • Pay for routine effort: • Avg. Profit = (.6)600,000 – 100,000 = $260,000 • Pay additional $50K for high effort: • Avg. Profit = (.8)600,000 – 150,000 = $330,000 • If effort is observable, pay for high effort • Expected Profit = $330K

24. Problems • Fixed payment scheme offers no incentives for high effort • High effort is more profitable • Worst case scenario: $260K • Effort-based scheme cannot be implemented • Cannot monitor firm effort • Best case scenario: $330K • Question: how close can we get to best case scenario if effort is unobservable? • Next time…