Game theory v. price theory

Game theory

• Focus: strategic interactions between individuals.

• Tools: Game trees, payoff matrices, etc.

• Outcomes: In many cases the predicted outcomes are Pareto inefficient.

• But remember the Coase Theorem!

Price theory

• Focus: market interactions between many individuals.

• Tools: supply and demand curves

• Outcomes: In many cases the predicted outcomes are Pareto efficient. (This is the working of the invisible hand.)

• But remember the underlying assumptions and what can go wrong…

Assumptions of price theory

1. Each buyer and seller is small relative to the size of the market as a whole, and so each buyer and seller is a price-taker who takes the market price as given.

2. Complete markets: there are markets for all goods (and therefore no externalities).

3. Complete information: Buyers and sellers have no private information.

Price-taking assumption

• Each buyer and seller is small relative to the size of the market as a whole, and so each buyer and seller is a price-taker who takes the market price as given.

• If this assumption is not met, some buyers and/or sellers have market power, e.g., monopoly, monopsony, duopoly, etc.

• Resulting inefficiencies?

Complete markets assumption

• Complete markets: there are markets for all goods (and therefore no externalities).

• If this assumption is not met, there are externalities, either positive or negative.

• Resulting inefficiencies?

Complete information assumption

• Complete information: Buyers and sellers have no private information.

• If this assumption is not met, there can be asymmetric information.

• Resulting inefficiencies?

• Example: the market for lemons (from Akerlof’s Nobel Prize-winning paper)

The market for lemons

• Consider a used car market in which sellers know the quality of their car, but buyers cannot tell if a given car is a peach or a lemon.

• What is the effect of this asymmetric information on the market?

• Until Akerlof’s paper, economists thought that there was no major effect.

A numerical example

• Imagine that sellers’ cars are equally divided among 4 values: $4800 (the peaches), $2300, $1500, and $1000 (the lemons).

• Buyers cannot distinguish between them, so they’re only willing to pay the average value (i.e., expected value) for a used car.

• What is the expected value if all 4 types of cars are sold?

Expected value if $1000/$1500/ $2300/$4800 cars are all sold?

$1,500 $2,000 $2,400 $2,800 $3,300 $4,200

0% 0% 0%0%

10%

90%1. $1500

2. $2000

3. $2400

4. $2800

5. $3300

6. $4200

A numerical example

• Sellers’ cars are equally divided among 4 values: $4800 (the peaches), $2300, $1500, and $1000 (the lemons).

• If all 4 types of cars are sold, buyers are only willing to pay the average value (i.e., expected value) for a used car: $2400.

• But sellers of $4800 cars (the peaches) won’t sell for this amount!

A numerical example

• We can’t have a market where all 4 types of cars are sold, but maybe we can have a market where 3 types are sold: $2300, $1500, and $1000 (the lemons).

• Again, buyers are only willing to pay the average value (i.e., expected value). What is that value if cars are equally divided between these 3 types?

Expected value if $1000/$1500/ $2300 cars are all sold?

$1,000 $1,200 $1,400 $1,600 $1,800 $2,000

0% 0% 0%0%

100%

0%

1. $1000

2. $1200

3. $1400

4. $1600

5. $1800

6. $2000

A numerical example

• We can’t have a market where even 3 types of cars are sold, but maybe we can have a market where 2 types are sold: $1500, and $1000 (the lemons).

• Again, buyers are only willing to pay the average value (i.e., expected value). What is that value if cars are equally divided between these 2 types?

Expected value if $1000/$1500/ cars are all sold?

$1,100 $1,250 $1,400

2% 0%

98%1. $1100

2. $1250

3. $1400

The market for lemons

• In the numerical example, we have complete unraveling and only the worst-quality cars (the lemons) are sold. This is called adverse selection because the cars that are sold appear to be selected adversely.

• A more important example of adverse selection: health insurance.

A numerical example

• Imagine that consumers’ likely health care expenditures are equally divided among 4 values: $200, $2700, $3500, and $4000.

• Insurance companies cannot distinguish between them, so in order to avoid losing money they have to charge at least the average cost for health insurance.

• Who are the peaches and who are the lemons?

Who are the peaches and who are the lemons?

Peaches are $200,lemons are $4000.

Peaches are$4000, lemons are

$200.

10%

90%1. Peaches are

$200, lemons are $4000.

2. Peaches are $4000, lemons are $200.

A numerical example

• Consumers’ likely health care expenditures are equally divided among 4 values: $200, $2700, $3500, and $4000.

• If all 4 types of consumers buy health insurance, companies have to charge at least the average cost, ¼(200)+¼(2700) +¼(3500)+¼(4000) = $2600.

• But the peaches won’t pay that much!

A numerical example

• So maybe we can have a market where 3 types buy insurance: $2700, $3500, and $4000.

• Again, insurance companies have to charge at least the average cost, which is 1/3(2700)+1/3(3500)+1/3(4000)=3400.

• Again, the low cost buyers will choose to self-insure.

A numerical example

• We can’t have a market where even 3 types of consumers buy insurance, but maybe we can have a market with 2 types are sold: $3500 and $4000 (the lemons).

• But insurance companies must charge at least the average cost ($3750) and at this price the lower-cost consumers will self-insure, leaving only the lemons.

Assumptions of price theory

1. Each buyer and seller is small relative to the size of the market as a whole, and so each buyer and seller is a price-taker who takes the market price as given.

2. Complete markets: there are markets for all goods (and therefore no externalities).

3. Complete information: Buyers and sellers have no private information.