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

2. 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

3. Signaling Definition Requires
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!
Mike Shor

4. 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
Mike Shor

5. 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
Mike Shor

6. Cost of No Deductible If the cost of avoiding a deductible is
Less than $200
Both types buy
Pooling Equilibrium
Greater than $500
Neither type buys
Pooling equilibrium
Between $200 and $500
Only high risk drivers buy
Separating equilibrium
Mike Shor

7. Pooling Insurance company charges $200
Both types buy
Expected profit for insurance company:
High risk drivers:
$200 - (30%) $1,000 = $200 - $300 = -$100
Low risk drivers:
$200 - (10%) $1,000 = $200 - $100 = $100
Profitable only if there are more low-risk drivers than high-risk drivers
Mike Shor

8. Separating Insurance company charges $500 Always profitable
Only high-risk drivers buy
Expected profit for insurance company:
High risk drivers:
$500 - (30%) $1,000 = $500 - $300 = $200
Low risk drivers: $0
Always profitable
Mike Shor

9. 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
Mike Shor

10. 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
Mike Shor

11. Adverse Selection Imagine ½ of the population are high-risk drivers
Insurance company calculates expected cost of not having a deductible:
(1/2) (10%) $ (1/2) (30%) $1000
= $200
Add a 10% profit, charge $220
Only high risk drivers sign up!
Mike Shor

12. 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
Mike Shor

13. 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
Mike Shor

14. Example: Econ majors How hard should an econ major be?
Two types of workers:
High and low quality
NPV of salary
high quality worker: $900,000
low quality worker: $700,000
Disutility per econ credit
high quality worker: $4,000
low quality worker: $6,000
Mike Shor

15. “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, > 4,000 N
50 credits > N
Mike Shor

16. “Low” Quality Workers 900,000 – 6,000 N < 700,000
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, < 6,000 N
33 credits < N
Mike Shor

17. 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
Mike Shor

18. 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
Mike Shor

19. Screening Solves Market Imperfections
Market for lemons (used cars)
Worth between $1000 and $3000 to buyers
Worth $200 less to sellers
Only seller knows true value
Buyer offers $2,000  Adverse selection
Only cars between $1,000 and $2,200 sold
Buyer offers $1,600  Adverse selection
Only cars between $1,000 and $1,800 sold
Market equilibrium price: $1,200
Only worst 20% of cars are ever sold
Mike Shor

20. 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
Mike Shor

21. 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
Mike Shor

22. 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!
Mike Shor

23. Summary Enticing high effort is hard work Screening Leakages
Global vs. individual incentives
Rewarding the right people
Screening
Identify unobservable cost differences
Exploit them (carefully)
Mike Shor