Game Theory A little knowledge is a dangerous thing. So is a lot. - Albert Einstein Topic 7...
Transcript of Game Theory A little knowledge is a dangerous thing. So is a lot. - Albert Einstein Topic 7...
Game Theory
“A little knowledge is a dangerous thing.
So is a lot.”- Albert Einstein
Topic 7Information
Strategic Use of Information
Incentive SchemesCreating situations in which observable
outcomes reveal the unobservable actions of the opponents.
ScreeningCreating situations in which the better-informed
opponents’ observable actions reveal their unobservable traits.
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Signaling
Definition Using actions that other players would
interpret in a way that would favor you in the game play
Requires It is not in the best interest for people to
signal falsely Implies signaling must be costly!
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Auto Insurance
A $1,000 deductible?
High risk drivers: 30% chance of claim Risk aversion: willing to pay $500
Low risk drivers: 10% chance of claim Risk aversion: willing to pay $200
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Pooling vs. Separating
A pooling equilibrium has all types taking the same action Therefore, cannot distinguish types by the
actions they take A separating equilibrium has different
types taking different actions Therefore, can distinguish types by the
actions they take
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Cost of No Deductible
If the cost of avoiding a deductible is Less than $200
Both types buyPooling Equilibrium
Greater than $500Neither type buysPooling equilibrium
Between $200 and $500Only high risk drivers buySeparating equilibrium
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Pooling
Insurance company charges $200 Both types buy Expected profit for insurance company:
High risk drivers:
$200 - (30%) $1,000 = $200 - $300 = -$100Low risk drivers:
$200 - (10%) $1,000 = $200 - $100 = $100
Profitable only if there are more low-risk drivers than high-risk drivers
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Separating
Insurance company charges $500 Only high-risk drivers buy Expected profit for insurance company:
High risk drivers:
$500 - (30%) $1,000 = $500 - $300 = $200Low risk drivers: $0
Always profitable
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Comparing Equilibria
Imagine that p proportion are high-risk Insurance company charges $200
Profit: $100 (1-p) - $100 p = $100-$200p Insurance company charges $500
Profit: $200p Compare:
$200p > $100-$200p p > ¼ better to separate than pool
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Self-Selection
Only high risk drivers “self-select” into the contract to buy insurance
Screening sets up the proper incentives for individuals to self-select
Pooling has the danger of adverse selection
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Adverse Selection
Imagine ½ of the population are high-risk drivers
Insurance company calculates expected cost of not having a deductible:
(1/2) (10%) $1000 + (1/2) (30%) $1000
= $200 Add a 10% profit, charge $220 Only high risk drivers sign up!
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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
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Screening
Education as a signaling and screening device
Is there value to an economics degree?
Imagine not: no effect on productivity, but is observed by
employers “Cost” of economics major varies
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Example: Econ majors
How hard should an econ major be? Two types of workers:
High and low quality NPV of salary
high quality worker: $900,000low quality worker: $700,000
Disutility per econ credithigh quality worker: $4,000low quality worker: $6,000
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“High” Quality Workers
If I get an econ major: Signal I am a high quality worker Receive $900,000 - $4,000 N
If I don’t get an econ major Signal I am a low quality worker Receive $700,000
900,000 – 4,000 N > 700,000
200,000 > 4,000 N
50 credits > N
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“Low” Quality Workers
If I get an econ major: Signal I am a high quality worker Receive $900,000 - $6,000 N
If I don’t get an econ major Signal I am a low quality worker Receive $700,000
900,000 – 6,000 N < 700,000
200,000 < 6,000 N
33 credits < N
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Screening
To achieve a separating equilibrium: Costly enough to deter low types Not so costly as to deter high types
High reward High reward
– high-type cost – low-type cost
> Low reward < Low reward
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Screening
To achieve a separating equilibrium: High types work for high reward Low types accept low reward
High reward High reward
– Low reward – Low reward
> high-type cost < low-type cost
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Screening Solves Market Imperfections
Market for lemons (used cars)Worth between $1000 and $3000 to buyersWorth $200 less to sellersOnly seller knows true value
Buyer offers $2,000 Adverse selectionOnly cars between $1,000 and $2,200 sold
Buyer offers $1,600 Adverse selectionOnly cars between $1,000 and $1,800 sold
Market equilibrium price: $1,200Only worst 20% of cars are ever sold
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Screening Solves Market Imperfections
Market for lemons What about introducing a screen? Extended warranty
Cheaper to provide for good cars than bad cars
Other examples Coupons Banks made of granite
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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
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Hiding from Signals
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!
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Summary
Enticing high effort is hard work Leakages Global vs. individual incentives Rewarding the right people
Screening Identify unobservable cost differences Exploit them (carefully)
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