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

2 Strategic Manipulation of Information Strategies for the less informed Incentive Schemes Screening Strategies for the more informed Signaling Signal Jamming

3 Less-informed Players Incentive Schemes Creating situations in which observable outcomes reveal the unobservable actions of the opponents. Screening Creating situations in which the better- informed opponents ’ observable actions reveal their unobservable traits.

4 Less-informed Players Screen Incentive

5 Moral Hazard & Roulette $50

6 Risk Aversion RiskRiskRisk SeekingNeutralAverse Lottery Corporations (small stakes) one-time deals Multiple Insurance Gambles (big stakes)

7 Multiple Gambles (biased) coin flip 52%-48% Chance of Loss 48%

8 10 tosses Chance of Loss 32%

tosses Chance of Loss 9%

10 Moral Hazard A project with uncertain outcome Probability of success depends on firm ’ s effort prob. of success = 0.6 if effort is routine prob. of success = 0.8 if effort is high Firm has cost of effort cost of routine effort= $100,000 cost of high effort = $150,000 project outcome = $600,000 if successful

11 Compensation Schemes I.Fixed Payment Scheme II.Observable Effort III.Bonus Scheme IV.Franchise Scheme

12 Incentive Scheme 1: Fixed Payment Scheme If firm puts in routine effort: Utility = Payment - $100,000 If firm puts in high effort: Utility = Payment - $150,000 Firm puts in low effort! Value of project = (.6)600,000 = $360,000 Optimal Payment: lowest possible. Payment = $100,000 Expected Profit = $360 - $100 = $260K

13 Incentive Scheme 2 Observable Effort Firm puts in the effort level promised, given its pay Pay for routine effort: E[Profit] = (.6)600,000 – 100,000 = $260,000 Pay additional $50K for high effort: E[Profit] = (.8)600,000 – 150,000 = $330,000 If effort is observable, pay for high effort Expected Profit = $330K

14 Problems Fixed payment scheme offers no incentives for high effort High effort is more profitable Effort-based scheme cannot be implemented Cannot monitor firm effort

15 Incentive Scheme 3 Wage and Bonus Suppose effort can not be observed Incentive-Compatible compensation Compensation contract must rely on something that can be directly observed and verified. Project ’ s success or failure Related probabilistically to effort Imperfect but positive information

16 Observable Outcome Incentive Compatibility It must be in the employee ’ s best interest to put in high effort Participation Constraint Expected salary must be high enough for employee to accept the position

17 Incentive Compatibility Compensation Package (s, b) s: base salary b: bonus if the project succeeds Firm ’ s Expected Earnings routine effort: s + (0.6)b high-quality effort: s + (0.8)b

18 Incentive Compatibility Firm will put in high effort if s + (0.8)b - 150,000 ≥ s + (0.6)b - 100,000 (0.2)b ≥ 50,000 marginal benefit of effort > marginal cost b ≥ $250,000

19 Participation The total compensation should be good enough for the firm to accept the job. If incentive compatibility condition is met, the firm prefers the high effort level. The firm will accept the job if: s + (0.8)b ≥ 150,000

20 Enticing High Effort Incentive Compatibility: Firm will put in high effort if b ≥ $250,000 Participation: Firm will accept contract if s + (0.8)b ≥ 150,000 Solution Minimum bonus: b = $250,000 Minimum base salary: s = 150,000 – (0.8)250,000 = -$50,000

21 Negative Salaries ? Ante in gambling Law firms / partnerships Work bonds / construction Startup funds Risk Premium !!!

22 Interpretation $50,000 is the amount of capital the firm must put up for the project $50,000 is the fine the firm must pay if the project fails. Expected profit: (.8)600,000 – (.8)b – s = (.8)600,000 – (.8)250, ,000 = $330,000 Same as with observable effort!!!

23 Negative Salaries? Not always a negative salary, but: 1. Enough outcome-contingent incentive (bonus) to provide incentive to work hard. 2. Enough certain base wage (salary) to provide incentive to work at all. 3. Optimally, charge implicit “ risk premium ” to party with greatest control.

24 Incentive Scheme 4 Franchising Charge the firm f regardless of profits Contractee takes all the risks and becomes the “ residual owner ” or franchisee Charge franchise fee equal to highest expected profit Routine effort:.6(600K)-100K = 260K High effort:.8(600K)-150K = 330K Expected Profit: $330K

25 Summary of Incentive Schemes Observable Effort Expected Profit: 330K Expected Salary: 150K Salary and Bonus Expected Profit: 330K Expected Salary: 150K Franchising Expected Profit: 330K Expected Salary: 150K

26 Uncertainty and Risk COMMANDMENT In the presence of uncertainty: Assign the risk to the better informed party. Efficiency and greater profits result. The more risks are transferred to the well- informed party, the more profit is earned.

27 Risks Employees (unlike firms) are rarely willing to bare high risks Salary and Bonus 0.8 chance: 200K 0.2 chance –50K Franchising 0.8 chance: 270K 0.2 chance –330K

28 Summary Can perfectly compensate for information asymmetry Let employee take the risk (franchising) Make employee pay you a “ moral hazard premium ” (salary and bonus) Usually, this is unreasonable To offer a reasonable incentive-compatible wage, must pay a cost of information asymmetry born by less-informed party

29 Cost of Information Asymmetry Want to reward high effort Can only reward good results How well are results tied to effort? Bayes rule: How well results are linked to effort depends on Likelihood of success at different effort levels Amount of each effort level in the population

30 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 You test positive! Are you worried?

31 Bayes Rule What is the chance that you have the disease if you tested positive? InfectedNot Infected 11,000,000 95% test pos.5% test pos. ______________________________________________________________________________________  150,000 Chance: 1 in 50,000

32 Example: HMOs HMOs costs arise from treating members: routine visits and referrals Moral hazard: “ necessity of treatment ” is unobservable Incentive scheme: Capitation: fixed monthly fee per patient Withholds: charges to the doctor if referred patients spend more than in a “ withhold fund, ” bonuses if they spend less.

33 Better-informed Players Signaling Using actions that other players would interpret in a way that would favor you in the game play Signal-jamming Using a mixed-strategy that interferes with the other players ’ inference process Other players would otherwise find out things about you that they could use to your detriment in the game.

34 Screening & Signaling 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

35 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?

36 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

37 Adverse Selection Expected cost of accidents in population (½.9 + ½.1 )10,000= $5,000 Expected cost of accidents among 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)

38 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

39 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

40 Screening Education as a signaling and screening device Is there value to education? Good types: less hardship cost

41 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

42 “ High ” Quality Workers If I get an MBA (signal “ good ” type): 1,600,000 – 5,000N If I don ’ t get an MBA ( “ bad ” type): 1,000,000 1,600,000 – 5,000N > 1,000, ,000 > 5,000N 120 > N

43 “ Low ” Quality Workers If I get an MBA (signal “ good ” type): 1,600,000 – 20,000N If I don ’ t get an MBA ( “ bad ” type): 1,000,000 1,600,000 – 20,000N < 1,000, ,000 < 20,000N 30 < N

44 Signaling The opportunity to signal may prevent some types from hiding their characteristics Pass / Fail grades (C is passing)

45 Screening 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!

46 Market for Lemons Used car market ½ of cars are “ mint ” worth $1000 to owner, $1500 to buyer ½ of cars are “ lemons ” worth $100 to owner, $150 to buyer I make a take-it-or-leave it offer If I offer 100 < p < 1000, only “ lemons ” Might as well offer p=100 If I offer p > 1000 everyone accepts On average, car is worth: ½(1500) + ½(150) = 825 < 1000

47 Market for Lemons Only outcome: offer $100 Unraveling of markets Inefficient resale price of slightly used cars Need to create signals Inspection by mechanics Warranties Dealer reputation

48 Summary If less informed Provide contracts which encourage optimal behavior on the part of the well-informed Create costly screens which allow the types to self-select different signals If more informed Invest in signals to demonstrate traits If market suffers from lack of info Create mechanisms for information revelation