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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