Game Theory
Mike Shor
Lecture 9
“I like work. It fascinates me.
I can sit and look at it for hours.”
- Jerome Klapka Jerome
Strategic Manipulation
of Information
Strategies for the less informed
IncentiveSchemes
Screening
Strategies for the more informed
Signaling
Signal Jamming
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Game Theory & Business Strategy
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.
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Game Theory & Business Strategy
Moral Hazard & Roulette
$50
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Game Theory & Business Strategy
Risk Aversion
Risk Risk Risk
Seeking Neutral Averse
Lottery Corporations
(small stakes) one-time deals
Multiple Insurance
Gambles (big stakes)
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Game Theory & Business Strategy
Biased coin flip:
52%-48%
Would you bet $1000 on it?
Chance
0.6
0.5
0.4
of Loss
0.3
48%
0.2
0.1
0
-$1,000.00 $1,000.00
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Game Theory & Business Strategy
Biased coin flip:
52%-48%
Would you bet $100 on it 10 times?
0.25
0.2 Chance
0.15
of Loss
0.1 33%
0.05
0
-$1,000.00 $0.00 $1,000.00
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Game Theory & Business Strategy
Biased coin flip:
52%-48%
Would you bet $1 on it 1000 times?
0.03
Chance
0.02 of Loss
0.01
10%
0
-$100.00 $0.00 $100.00
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
Compensation Schemes
Benchmarks:
FixedPayment
Observable Effort
Result-contingent bonus scheme
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
Incentive Scheme 1:
Fixed Payment
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
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
Problems
Fixed payment scheme offers no incentives
for high effort
Higheffort 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?
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
Observable Outcome
Incentive Compatibility
Putting in high effort must be better
than putting in low effort
Participation Constraint
Putting in any effort must be better
than not taking the position
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Game Theory & Business Strategy
Incentive Compatibility
Compensation Package (f, b)
f: fixed base payment
b: bonus if the project succeeds
Firm’s Expected Earnings
routineeffort: f + (0.6)b
high-quality effort: f + (0.8)b
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
Incentive Compatibility
Firm will put in high effort if
b ≥ $250,000
Our profit maximization means that we
want to set b as low as possible
b = $250,000
Next, solve participation constraint
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Game Theory & Business Strategy
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:
f + (0.8)b ≥ 150,000
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
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
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Game Theory & Business Strategy
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.
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Game Theory & Business Strategy
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 + 50,000
= $330,000
Same as with observable effort!!!
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Game Theory & Business Strategy
Moral Hazard
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.
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Game Theory & Business Strategy
Moral Hazard
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.
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Game Theory & Business Strategy
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)
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Game Theory & Business Strategy
Summary
Can perfectly compensate for
information asymmetry
Letemployee 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
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Game Theory & Business Strategy