Game Theory “A little knowledge is a dangerous thing. So is a lot.” - Albert Einstein Topic 7 Information

Strategic Use of Information 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. Mike Shor 2

Moral Hazard & Roulette Mike Shor 3 $50

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 Mike Shor 4

Compensation Schemes Benchmarks:  Fixed Payment  Observable Effort Result-contingent bonus scheme Mike Shor 5

Incentive Scheme 1: Fixed Payment A fixed payment must be high enough to get the firm to accept the project No amount of fixed payment can change the firm’s behavior once it accepts the project Mike Shor 6

Incentive Scheme 1: Fixed Payment For any fixed payment, effort will be low:  Payment - $100,000 > Payment - $150,000 Optimal Payment  Lowest possible  Firm requires at least $100,000  Payment = $100,000 Expected Profit  Value of project— payment = (.6) $600K— $100K = $360 - $100 = $260K Mike Shor 7

Incentive Scheme 2: Observable Effort If we can observe effort, contracts are simple:  Work as hard as we tell you to, or you are fired Only question: How hard do we want employees to work?  Remember, salary must be commensurate with level of effort, or no one will take the job Mike Shor 8

Incentive Scheme 2: Observable Effort Firm puts in the effort level promised, given its 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 Mike Shor 9

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? Mike Shor 10

Incentive Scheme 3: Fixed Payment 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 Mike Shor 11

Observable Outcome Incentive Compatibility (high > low)  Putting in high effort must be better than putting in low effort Participation Constraint (high > none)  Putting in high effort must be better than not taking the contract Mike Shor 12

Incentive Compatibility Compensation Package (f, b)  f: fixed base payment  b: bonus if the project succeeds Mike Shor 13

Incentive Compatibility If Firm puts in high effort  80% chance of bonus, cost of $150K  Profit: f + (0.8)b – 150K If Firm puts in low effort  60% chance of bonus, cost of $100K  Profit: f + (0.6)b – 100K If Firm does not take contract  Profit: 0 Mike Shor 14

Incentive Compatibility Firm will put in high effort if f + (0.8)b - 150,000 ≥ f + (0.6)b - 100,000  (0.2)b ≥ 50,000 marginal benefit of effort > marginal cost  b ≥ $250,000 Mike Shor 15  (high > low)

Incentive Compatibility Firm will put in high effort if b ≥ $250,000 To maximize profit, set b as low as possible b = $250,000 Next, solve participation constraint Mike Shor 16

Participation The total compensation should be good enough for the firm to accept the job. Want firm to prefer high effort to none. The firm will accept the job if: f + (0.8)b -150,000 ≥ 0 Mike Shor 17  (high > none)

Participation Firm will accept contract if expected pay is greater than cost f + (0.8)b ≥ 150,000 Solution  Substitute minimum bonus: f + (0.8)250,000 ≥ $150,000 f + $200,000 ≥ $150,000 f ≥ – $50,000 Mike Shor 18

Negative Fixed Payment? Certainly not for normal employees  Ante in gambling  Law firms / partnerships  Work bonds / construction  Startup funds Interpretation:  Capital the firm must put up for the project  Fine the firm must pay if the project fails.  Risk premium Mike Shor 19

Negative Fixed Payment? Fixed payment not always negative, 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. Implicitly charging a “risk premium” to party with greatest control. Mike Shor 20

Benchmarks Fixed payment scheme:  Worst case scenario: $260K Effort-based scheme:  Best case scenario: $330K Fixed payment and bonus: Exp. Profit = (.8)600,000 – (.8)b – f = (.8)600,000 – (.8)250, ,000 = $330,000 Same as with observable effort!!! Mike Shor 21

Moral Hazard Mike Shor 22 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.

Moral Hazard Mike Shor 23 CAVEAT In the presence of uncertainty: Assign the risk to the better informed party. Efficiency and greater profits result. BUT If done imprecisely, may be better not to bother.

Negative Fixed Payment? Bonus depends on  difference between low and high effort costs Fixed payment depends on  absolute magnitude of costs Example: Firm has cost of effort  cost of routine effort= $250,000 (+$150K)  cost of high effort = $300,000 (+$150K)  BONUS UNCHANGED(b =$250,000)  FIXED INCREASES (f = $100,000) Mike Shor 24

Summary Can perfectly compensate for information asymmetry  Let employee take the risk  Use two part contracts (salary and bonus) Often, this is unreasonable  Employees unwilling to assume risks  Contracts must be perfectly balanced  May be better to settle for low effort Mike Shor 25

Risk Aversion Mike Shor 26 Risk Risk Risk Seeking Neutral Averse Lottery Corporations (small stakes) one-time deals Multiple Insurance Gambles (big stakes)

Biased coin flip: 52%-48% Would you bet $1000 on it? Mike Shor 27 Chance of Loss 48%

Biased coin flip: 52%-48% Would you bet $100 on it 10 times? Mike Shor 28 Chance of Loss 33%

Biased coin flip: 52%-48% Would you bet $1 on it 1000 times? Mike Shor 29 Chance of Loss 10%