1. Econ 522 Economics of Law
Dan Quint
Spring 2017
Lecture 7

2. Monday, we “tested the Coase Theorem”
Can UW undergrads reallocate poker chips efficiently?
(Cost me $124 to find out)
What happened?

3. actual final allocation fraction of potential gains realized
Our experiment…
Take 1: Full Information (values on nametags)
starting allocation
efficient allocation
actual final allocation
fraction of potential gains realized 12
red chip
purple chip 10
purple chip
purple chip 10
purple chip
purple chip 8
red chip
purple chip
red chip 8
purple chip 6
purple chip
purple chip 6 4
purple chip 4
purple chip 2
purple chip 32 60 54
22/28 = 79%

4. actual final allocation fraction of potential gains realized
Our experiment…
Take 2: Private Information (values hidden)
starting allocation
efficient allocation
actual final allocation
fraction of potential gains realized 10
red chip
red chip 8
purple chip
purple chip 8
purple chip
purple chip 6
red chip
purple chip 6
purple chip
purple chip 4
purple chip
purple chip 4 3
purple chip 3
purple chip 2
purple chip 24 48 46
22/24 = 92%

5. Our experiment… Take 3: Uncertainty Take 4: Asymmetric Information
Rolled 3 – chip worth 6 to seller, 9 to buyer
Chip traded
So we achieved 100% of gains from trade!
(Seller accepted less than expected value)
Take 4: Asymmetric Information
Rolled 5 – worth 10 to seller, 15 to buyer
Chip traded (for 11), so we achieved all the gains!
(Big leap of faith for buyer to pay 11, but it worked out)

6. Conclusion
Coase seems to work pretty well – even when there are potential information problems!
Full info: 79% of gains achieved
Private info: 92% of gains
Uncertainty: 100%
Asymmetric info: 100%
But that’s in a pretty idealized environment

7. Question to ponder
“Recharge shop” owners in India are saving women’s numbers when they add mobile minutes, selling them to harassers
What would the Coase Theorem say about efficient “ownership” of knowledge of someone’s phone number?
Does Coase apply here? Why/why not?
What remedy would make sense here?
Source:
The Hindustan Times reports the following scam occurring in Uttar Pradesh, the Indian province southwest of Delhi. Many small “recharge shops” exist where people can add minutes to their prepaid mobile phones; some shop owners have begun to save the numbers of girls and women who recharge there, and then sell the numbers to men, who call to harass the women, often with the opening line “I want to make friendship with you”. The phone number of an “ordinary-looking girl” sells for below a dollar, while the phone number of someone “beautiful” sells for about $7.50.

8. what can be privately owned? what can an owner do?
Monday: starting thinking about details of efficient property law system
what can be privately owned?
what can an owner do?
how are property rights established?
what remedies are given?
We said that any property rights system must address four questions:
What things can be privately owned?
What can (or can’t) an owner do with his/her property?
How are property rights established?
And what remedies are given when they are violated?
Last time, we addressed the fourth question – remedies – and concluded that:
When TC are low, injunctive relief
When TC are high, damages

9. Monday: starting thinking about details of efficient property law system
Calabresi/Melamed: three types of remedies
Injunctive relief (property rule) – violations prohibited without prior permission, punished severely, but tradable
Damages (liability rule) – violations compensated
Inalienability – violations punished, not tradable
Inalienability…
Might make sense when allocation involves large externalities that can’t be overcome
Might be a product of governmental paternalism…
…or legislator (or voter) repugnance 8 8

10. Monday: starting thinking about details of efficient property law system
When transaction costs are low, use injunctive relief
Either rule will lead to efficient allocation (Coase)…
…but injunctions are cheaper to implement
(court doesn’t have to assess level of harm)
When transaction costs are high, use damages
If bargaining is impossible, damages  more efficient outcomes
(Example: polluter can choose to pollute and pay when that’s more efficient than preventing the damage)
Agrees with principle from last week
TC low: design law to facilitate trade (normative Coase)
TC high: design law to not rely on bargaining (normative Hobbes) 9 9

11. Onward!
what can be privately owned?
what can an owner do?
how are property rights established?
what remedies are given?

12. Public versus Private Goods
rivalrous – one’s consumption precludes another
excludable – technologically possible to prevent consumption
example: apple
Public Goods
non-rivalrous
non-excludable
examples
defense against nuclear attack
infrastructure (roads, bridges)
parks, clean air, large fireworks displays
You may recall from micro a discussion of Public and Private Goods.
Private Goods tend to be characterized by two properties:
Rivalrous – one person’s consumption of a private good precludes another person’s enjoyment of its benefits
if I eat an apple, you won’t be able to eat that same apple
Excludable – it’s technologically possible to prevent others from consuming it
It shouldn’t be too hard for me to prevent you from eating it.
Public Goods tend to be characterized by the opposite of these two properties:
Nonrivalrous – one person’s consumption of a public good does not impact others’ enjoyment of it
Nonexcludable – hard to prevent people from taking advantage
The cleanest example of a public good is defense against a nuclear attack
It’s very hard for me to defend myself from a nuclear attack in a way that doesn’t also protect you a bit
and you being safe from nuclear attack doesn’t impact my enjoyment of this privilege.
Other public goods are urban infrastructure (bridges and roads) (although roads may become somewhat rivalrous when there is congestion); parks, clean air, the ocean, fireworks displays (like on the homework), and so on.

13. Public versus Private Goods
When private goods are owned publicly, they tend to be overutilized/overexploited
A principle you may remember from intermediate micro: When private goods are owned publicly, they tend to be overutilized, or overexploited.
This is the point of the Hardin paper, the tragedy of the commons
His example: a large common area where everyone is permitted to graze their cattle
Since it’s public, nobody considers the cost their herd imposes on the grass
So the grass on the commons gets wiped out by overgrazing
Same problem as overfishing in the communal lake
Or overhunting in unregulated public land
Another example of this is congestion on busy roads
Most roads are provided publicly (no toll, free to use)
When there’s lots of traffic, roads become rivalrous – the more people on the road, the less utility I get from driving on them – so they take on one of the characteristics of a private good
But when people are deciding whether or not to drive, they tend not to consider the externality that their choice to drive has on other drivers; so the roads get overused
(Some cities are looking at ways to solve this problem with congestion pricing – charging people to use the roads during peak hours, so that people internalize this externality.)

14. Public versus Private Goods
When private goods are owned publicly, they tend to be overutilized/overexploited
When public goods are privately owned, they tend to be underprovided/undersupplied
One the other hand, when public goods are privately owned, they face the opposite problem: they will be underprovided
You just saw an example of this: the fireworks problem on the homework
Fireworks are a public good; so if each person decides for himself how much to contribute, we get less than the efficient amount of fireworks
Another example of this would be artistic creations if they weren’t protected by intellectual property
Certainly, something like a song, or a book, is non-rivalrous
And technology has made these things much closer to non-excludable
If anyone could freely copy my song, or my book, once it’s written, then I might get very little reward for writing it; so I have little incentive to create, and might choose not to
Recall our earlier story of a hops farmer and a brewery
When there was a single hops farmer, he could negotiate with the brewery to reduce pollution and breathe cleaner air
But if the dirty air affects lots of people, it becomes a “public bad” – and if each person tries to negotiate separately with the brewery to reduce pollution, they will reduce it less than efficiency would suggest.

15. Public versus Private Goods
When private goods are owned publicly, they tend to be overutilized/overexploited
When public goods are privately owned, they tend to be underprovided/undersupplied
Efficiency suggests private goods should be privately owned, and public goods should be publicly provided/regulated
These two observations bring us to the following general rule:
Efficiency suggests that private goods should be privately owned, and public goods should be publicly provided or regulated
Private ownership of private goods avoids overuse, and allows trade, leading to efficient allocations (Coase)
Public provision of public goods avoids undersupply
This also gives us another interpretation of the Demsetz example we did last week, of the development of property rights to land among Native Americans
What makes the case interesting is that land can be either a public or a private good, depending on the circumstances.
National forests can be thought of as a public good
they’re a good thing ecologically, they’re pretty to drive by and hike in, I can enjoy them even if other people are enjoying them, and it’s hard to exclude other people from getting their benefits.
On the other hand, 900 square feet in the middle of a city is a private good
if I build an apartment there and live in it, that precludes you doing the same; and as long as I get a door with a decent lock, I can keep you out.
Demsetz’s observation was that property rights over land developed among Native Americans as the fur trade became more important economically
We can interpret this in terms of public and private goods.

16. Public versus Private Goods
When private goods are owned publicly, they tend to be overutilized/overexploited
When public goods are privately owned, they tend to be underprovided/undersupplied
Efficiency suggests private goods should be privately owned, and public goods should be publicly provided/regulated
Before the fur trade, land was pretty much a public good
There was no shortage of animals, so hunting grounds were not particularly rivalrous – I could hunt on your land, and still leave enough game for you to hunt the next day
With the emergence of the fur trade came stronger incentives for hunting
Fur-bearing animals became more valuable, so were hunted more, so became scarce, so the land became a rivalrous good – the more I hunted, the less luck you would have hunting on the same land
So the emergence of the fur trade led to a sort of transition of land from being a public to a private good
Efficiency would then suggest that at the same time, it should go from being publicly owned (everyone could hunt on it) to being privately owned (one family might have exclusive rights to hunt in a particular area)
Which is pretty much what happened
So the general principle is, private goods should be owned privately, and public goods should be publicly provided/regulated
The book mentions the move in the 1990s toward deregulation/privitization as an example of correcting a situation of private goods being publicly supplied
services that did not involve externalities, and could therefore be supplied by private industry, but for historical reasons were being run by the government
in the 1990s, there was a big movement to dismantle or sell off government monopolies on trains, planes, and other services worldwide.

17. This also accords with the principle from last week
Transaction costs low  facilitate voluntary trade
Private goods – low transaction costs
Private ownership facilitates trade
Transaction costs high  allocate rights efficiently
Public goods – high transaction costs
Public provision/regulation required to get efficient amount

18. A different view: transaction costs
Clean air
Large number of people affected  transaction costs high
 injunctive relief unlikely to work well
Still two options
One: give property owners right to clean air, protected by damages
Two: public regulation
Argue for one or the other by comparing costs of each
Damages: costs are legal cost of lawsuits or pretrial negotiations
Regulation: administrative costs, error costs if level is not chosen correctly
Cooter and Ulen also point out that in many cases, either type of ownership, public or private, will involve some transaction costs, and the case can be made for one or the other by considering the magnitude of these costs
(In fact, we can think of public goods as goods where costs of privately transacting are too high – enforcement costs are high because the good is nonexcludable, or bargaining costs are high because so many people are affected)
Consider again the example of clean air
If there are lots of consumers affected by pollution from a factory, injunctive relief is unlikely to work well, since transaction costs tend to be high when there are lots of parties affected
However, there are still two possible ways to maintain clean air
One way is to grant property owners the right to clean air, but protected by damages; so that a factory, if it felt it worthwhile, could choose to pollute and pay damages
Alternatively, clean air could be viewed as a public good, and regulated by a government agency
We can argue for the efficiency of one system or the other by comparing the magnitude of these transaction costs
In the case of damages, the transaction cost here would be the legal cost of these lawsuits, or pretrial negotiations, including the cost to the court of calculating damages
In the case of regulation, this would involve the administrative costs of setting up and running a government agency to regulate air quality, and could run the risk of the level of pollution not being the one that is socially optimal
Whichever costs would be lower, suggests which system would be more efficient 17 17

19. How do we design an efficient property law system?
what can be privately owned?
what can an owner do?
how are property rights established?
what remedies are given?
We’ve addressed two questions so far.
What can be privately owned? (In general, private goods should be privately owned, public goods should be publicly provided or regulated.)
What remedies should be given? (In general, injunctive relief when transaction costs are low, damages when transaction costs are high)

20. What can an owner do with his/her property?
For efficiency: principle of maximum liberty
Owners can do whatever they like with their property…
…provided that doesn’t interfere with others’ property or rights
That is, you can do anything you like so long as it doesn’t impose an externality (nuisance) on anyone else
Textbook: common law often approximates rule of maximum liberty
But does it really?
What about bans on repugnant markets?
And…
Next, we consider the question, what can an owner do with his property?
Efficiency suggests that anything that makes me better off, and doesn’t affect anyone else, is efficient
And so efficiency suggests the principle of maximum liberty
maximum liberty suggests that owners can do anything with their property that does not interfere with other peoples’ property or rights
that is, you can do anything you like with your property as long as it doesn’t impose an externality on anyone else
once one person’s actions begin to affect another, we run into what we’ve already been looking at – nuisance law
In the textbook, they make the case that the common law approximates the rule of maximum liberty, although I’m a bit skeptical
Legislatures may pass laws that impose further restrictions on what people can do with their property
In general, these laws are only efficient if the behavior they are restricting causes an externality.

21. “Maximum liberty” vs. government’s right to regulate
Ruling a few years ago by a Dane County judge
Plaintiffs argued they had a “fundamental right to own a cow, and to use their cows in a manner that does not cause harm to a third party”
Judge responded:
“Plaintiffs do not have a fundamental right to own and use a dairy cow or a dairy herd
Plaintiffs do not have a fundamental right to consume the milk from their own cow
Plaintiffs do not have a fundamental right to board their cow at the farm of a farmer
The private contract does not fall outside the scope of the States’ police power
Plaintiffs do not have a fundamental right to produce and consume the foods of their choice
DATCP has jurisdiction to regulate the Plaintiffs’ conduct”
Here’s an example, though, showing that while “maximum liberty” is a nice theoretical idea, it’s not a legal assumption
Plaintiffs owned a couple of cows for their own milk consumption, that they arranged to board at a local farm
Asked a judge to clarify that their arrangement was legal
In August 2011, he ruled against them
They requested a clarification, which he issued that September
The ruling is discussed here:
The discussion in the blog is rather one-sided. There may be a lot more going on here.
Might just be saying, can’t own a dairy farm and also segregate a couple cows for “personal use” that are exempt from usual rules.
There are likely legitimate reasons (food safety, animal cruelty) to regulate the dairy industry
And there may be good reasons to not draw a line between private ownership of a cow or two and running a dairy business
But the strength of the language with which the judge “smacked down” the plaintiff does underline the point that “maximum liberty” is not necessarily an accurate description of the world we actually live in
(Also: if the judge were applying a new regulation that had just passed after the plaintiffs already owned their cows, this could constitute a regulatory taking – but in this case, he’s applying preexisting regulations that the plaintiffs hoped wouldn’t apply to “private use” cows)

22. How do we design an efficient property law system?
what can be privately owned?
what can an owner do?
how are property rights established?
what remedies are given?
Finally, how are property rights established?

23. Fugitive property Hammonds v. Central Kentucky Natural Gas Co.
Central Kentucky leased land lying above natural gas deposits
Geological dome lay partly under Hammonds’ land
Central Kentucky drilled down and extracted the gas
Hammonds sued, claiming some of the gas was his
(Anybody see “There Will Be Blood”?)
Hammonds
Central KY
Fugitive property is property that moves around or has indefinite boundaries – like foxes or whales
Another example: natural gas
Hammonds v. Central Kentucky Natural Gas Company (1934)
The Central Kentucky Natural Gas Company leased tracts of land above deposits of natural gas
But the geological dome of natural gas lay partly under the land they were leasing, and partly under someone else’s land
When the company began extracting the gas, Hammonds, one of the other landowners, sued, claiming that some of the gas they were extracting came from under her land.
Anybody see the movie “There Will Be Blood”?
toward the end, Eli returns to town, wants to lease Daniel Day Lewis the last bit of land in town that he hasn’t yet drilled for oil on
Daniel Day Lewis points out the land is worthless – the oil moved around, and he was able to extract all of it through other land he had leased
(Then he makes a speech about drinking Eli’s milkshake, and then kills him with a bowling pin.)

24. Two principles for establishing ownership
First Possession
nobody owns fugitive property until someone possesses it
first to “capture” a resource owns it
Central Kentucky would own all the gas
Tied Ownership
ownership of fugitive property tied (linked) to something else – here, ownership of the surface
so ownership already determined before resource is extracted
Hammonds would own some of the gas, since under his land
principle of accession – a new thing is owned by the owner of the proximate or prominent property
There are two different principles for how to establish ownership of fugitive property:
first possession – fugitive property does not belong to anybody until someone extracts it, establishing ownership
tied ownership – ownership of fugitive property is tied to something else which is easier to establish – in this case, the owner of the surface under which the natural gas resides
Under first possession, Central Kentucky Natural Gas Company would be entitled to whatever gas it extracted
Under tied ownership, they would only be entitled to the gas under their own land, and Hammond’s claim would be valid
Tied ownership would also suggest that a landowner has rights to the foxes on his own land.
Tied ownership might suggest that if you’re at a baseball game and a foul ball lands on your seat, you have automatic rights to it
While first possession suggests that whoever grabs the ball owns it.
When tied ownership is used, both the common and civil law often tie ownership using the principle of accession
a new thing is owned by the owner of the “proximate or prominent” property, that is, the nearest (or most obvious) thing to link ownership to
for example, a newborn calf belongs to the owner of its mother
when a river shifts and creates new land, the owner of the river bank owns that new land
and the owner of a brand name tends to have the default right to the corresponding Internet address

25. First Possession versus Tied Ownership
simpler to apply – easy to determine who possessed property first
incentive to invest too much to early in order to establish ownership
example: $100 of gas, two companies drilling fast or slow
drilling slowly costs $5, drilling fast costs $25
drill same speed  each gets half the gas, one drills fast  75/25
Firm 2
First possession has the advantage of generally being very simple (and therefore cheap) to apply
Determining who first possessed property is usually straightforward
However, first possession also has a downside
It creates an incentive to invest too much too early, in order to establish ownership of a scarce resource
That is, firms might expend too many resources trying to establish first possession of a resource, leading to inefficiency
For example, imagine there is an underground natural gas deposit, and two firms lease land above the deposit
This would create a race between them, since the gas was a scarce resource that belonged to whoever possessed it first
This would lead to both firms to try to extract it inefficiently quickly, using means that are more expensive than necessary
Example: two firms drilling for $100 worth of gas; drilling slow costs $5, fast costs $25; if both do same speed, 50/50 split; if one does fast, 75/25. Game is:
Like prisoner’s dilemma, (fast, fast) is equilibrium, even though (slow,slow) is more efficient
So a first possession rule leads to inefficient investment in “possessory acts” – inefficient behavior designed just to claim a valuable resource first
Slow
Fast
45, 45
20, 50
Slow
Firm 1
50, 20
25, 25
Fast

26. First Possession versus Tied Ownership
simpler to apply – easy to determine who possessed property first
incentive to invest too much to early in order to establish ownership
Tied Ownership
encourages efficient use of the resource
but, difficulty of establishing and verifying ownership rights
Firm 2
Slow
Fast
Tied ownership avoids this problem
If the ownership of the property to which the rights are tied is already established, tied ownership creates the incentive for efficient use of the resource.
If the ownership of the natural gas is not in question, the firm can extract it by the most efficient means possible – there is no need to race to get it first
Suppose that due to their rights to the surface, each firm knows that however quickly they extract it, they have rights to have the gas
Now there’s no reason not to drill slowly
Modify the game, and note the new equilibrium
Similarly, if salmon belong to nobody until they’re caught, we expect overfishing;
But if salmon are the property of the owners of the stream where they spawn, the owners have no incentive to deplete the salmon by overfishing.
However, as we saw in the Hammonds case, tied ownership faces the difficulty of establishing and verifying ownership rights
it is impossible to figure out “which” part of the natural gas being extracted was under Central Kentucky’s land and which part was under Hammond’s
45, 45
45, 25
Slow
Firm 1
25, 45
25, 25
Fast

27. This brings us to the following tradeoff:
Rules that link ownership to possession have the
advantage of being easy to administer,
and the disadvantage of providing incentives for
uneconomic investment in possessory acts.
Rules that allow ownership without possession have
the advantage of avoiding preemptive investment
and the disadvantage of being costly to administer.
This brings us to the following tradeoff:
Rules that link ownership to possession have the advantage of being easy to administer and the disadvantage of providing incentives for uneconomic investment in possessory acts.
Rules that allow ownership without possession have the advantage of avoiding preemptive investment and the disadvantage of being costly to administer.
So the problem with a first-possession rule is it leads to an investment in possessory acts, which do not create any value, just transfer it

28. We’ve already seen two examples of this
“Fast fish/loose fish” and “the guy who kills a fox, owns it” are examples of a first possession rule
You can’t own a resource until you physically possess it
“Iron holds the whale” and “the guy chasing a fox owns it” are examples of a tied ownership rule
You can establish ownership of something before you actually possess it
(A harpoon, or chasing a fox, gives you a right to it)
More complicated/costly to enforce
“if the first seeing, starting, or pursuing such animals… should afford the basis of actions against others for intercepting and killing them, it would prove a fertile source of quarrels and litigation”
But avoids incentive to poach someone else’s resource
This tradeoff was at work in the fox-hunt case, Pierson v Post
Awarding the fox to Pierson, the interloper, links ownership to possession, which is the simpler rule
But it gives him an incentive to jump in at the end of the hunt, which is inefficient
Awarding the fox to Post, the hunter, allows ownership without possession
It avoids the incentive problem, but is more difficult to administer, since there is less of a “bright line” to mark when ownership is established and the claim of ownership is harder to prove
Similarly, recall that sperm whales are too fast and strong to hunt with harpoons tied to the ship
So if first possession (like fast fish/loose fish) were applied to sperm whales, every time a whale was injured and trailing drogues, you’d have a bunch of ships chasing after it, competing to be the first to secure it – clearly inefficient
From decision in Pierson v Post: “If the first seeing, starting, or pursuing such animals… should afford the basis of actions against others for intercepting and killing them, it would prove a fertile source of quarrels and litigation”

29. Another nice historical example: the Homestead Act of 1862
Meant to encourage settlement of the Western U.S.
Citizens could acquire 160 acres of land for free, provided
head of a family or 21 years old
“for the purpose of actual cultivation, and not… for the use or benefit of someone else”
had to live on the claim for 6 months and make “suitable” improvements
Basically a first possession rule for land – by living on the land, you gained ownership of it
Friedman: caused people to spend inefficiently much to gain ownership of the land
A nice historical example of this can be traced to the Homestead Act of 1862
The Homestead Act was meant to encourage people to settle the Western part of the U.S.
It allowed citizens to acquire up to 160 acres of public land, provided
the claimant was the head of a family or 21 year old
the claim was “for the purpose of actual cultivation, and not, either directly or indirectly, for the use or benefit of” someone else
the claimant had to live on the claim for 6 months and make “suitable” improvements before title was granted
These requirements were meant to prevent a mad rush to acquire land and do nothing with it
The Homestead Act was effectively a first possession rule – you could claim the land by living on it
We just saw that first possession rules lead to uneconomic investment in possessory acts
Friedman points out that the Homestead Act caused people to spend inefficiently much in order to claim land that would later become valuable
Quoting from Law’s Order (p 120):

30. Friedman on the Homestead Act of 1862
“The year is 1862; the piece of land we are considering is… too far from railroads, feed stores, and other people to be cultivated at a profit.
…The efficient rule would be to start farming the land the first year that doing so becomes profitable, say But if you set out to homestead the land in 1890, you will get an unpleasant surprise: someone else is already there.
…If you want to get the land you will have to come early. By farming it at a loss for a few years you can acquire the right to farm it thereafter at a profit.
“The year is 1862; the piece of land we are considering is beyond the margin of settlement, too far from railroads, feed stores, and other people to be cultivated at a profit.
As time passes and settlement expands, that situation changes. The efficient rule would be to start farming the land the first year that doing so becomes profitable, say But if you set out to homestead the land in 1890, you will get an unpleasant surprise; someone else is already there. Homesteading land that is already profitable to farm is an attractive proposition, since you not only make money in the process, you also end up with valuable real estate. When valuable rights are being given away for free, there is no shortage of takers.
If you want to get the land you will have to come early. By farming it at a loss for a few years you can acquire the right to farm it thereafter at a profit.

31. Friedman on the Homestead Act of 1862
How early will you have to come?
Assume the value of the land in 1890 is going to be $20,000, representing the present value of the profit that can be made by farming it from then on. Further assume that the loss from farming it earlier than that is $1,000 a year.
If you try to homestead it in 1880, you again find the land already taken. Someone who homesteads in 1880 pays $10,000 in losses for $20,000 in real estate – not as good as getting it for free, but still an attractive deal.
…The land will be claimed about 1870, just early enough so that the losses in the early years balance the later gains.
It follows that the effect of the Homestead Act was to wipe out, in costs of premature farming, a large part of the land value of the United States.”
How early will you have to come?
To make things simple, assume the value of the land in 1890 is going to be $20,000, representing the present value of the profit that can be made by farming it from then on. Further assume that the loss from farming it earlier than that is $1,000 a year.
If you try to homestead it in 1880, you again find the land already taken. Someone who homesteads in 1880 pays $10,000 dollars in losses for $20,000 in real estate – not as good as getting it for free, but still an attractive deal.
Working through the logic of the argument, we conclude that the land will be claimed about 1870, just early enough so that the losses in the early years balance the later gains.
It follows that the effect of the Homestead Act was to wipe out, in costs of premature farming, a large part of the land value of the United States.”

32. So, what does an efficient property law system look like?
What things can be privately owned?
Private goods are privately owned, public goods are publicly provided
What can owners do with their property?
Maximum liberty
How are property rights established?
(Tradeoff between first possession and tied ownership; more examples to come)
What remedies are given?
Injunctions when transaction costs are low; damages when transaction costs are high

33. Next up Next up: some applications of property law
But first, one more tool…

34. Sequential Rationality

35. Dynamic games and sequential rationality
Game theory we’ve seen so far: static games
“everything happens at once”
(nobody observes another player’s move before deciding how to act)
Dynamic games
one player moves first
second player learns what first player did, and then moves

36. Let’s go back to a game we’ve seen – the Battle of the Sexes
Player 2
Ballgame
Opera
6, 3
0, 0
Ballgame
Player 1
0, 0
3, 6
Opera
Now change the game so that player 1 moves first
Player 1 goes somewhere
Player 2 learns what 1 did, then decides where to go 35 35

37. Dynamic games are typically shown as “game trees”
PLAYER 1
Ballgame
Opera
PLAYER 2
PLAYER 2
Ballgame
Opera
Ballgame
Opera
(6, 3)
(0, 0)
(0, 0)
(3, 6)
A strategy is one player’s plan for what to do at each decision point he/she acts at
Player 1: “Ballgame” or “Opera”
Player 2’s strategy is more complicated – can depend on P1’s choice

38. We can expand the matrix to accommodate Player 2’s additional options
Ballgame, Ballgame
Ballgame, Opera
Opera, Ballgame
Opera, Opera
6, 3
6, 3
0, 0
0, 0
Ballgame
Player 1
0, 0
3, 6
0, 0
3, 6
Opera
Player 2 has four options
“Go to the ballgame no matter what”
“Go to the ballgame if P1 went to the ballgame, otherwise opera”
“Opera if P1 went to the ballgame, otherwise ballgame”
“Opera no matter what” 37 37

39. We can solve this game for equilibrium in the “usual” way
Player 2
Ballgame, Ballgame
Ballgame, Opera
Opera, Ballgame
Opera, Opera
6, 3
6, 3
0, 0
0, 0
Ballgame
Player 1
0, 0
3, 6
0, 0
3, 6
Opera
Three equilibria:
1 goes to ballgame, 2 plays “ballgame no matter what”
1 goes to ballgame, 2 plays “go wherever 1 went”
1 goes to opera, 2 plays “opera no matter what”
Are all of these “reasonable”? 38 38

40. Are all these equilibria “reasonable”?
Consider the equilibrium where
player 2 plans to go to the opera no matter what
player 1 therefore goes to the opera
Player 1 might wonder…
“Suppose I changed my mind and went to the ballgame.
Once I’m there, player 2 has to choose between sticking to the plan, going to the opera, and getting 0…
…versus following me to the ballgame and getting 3.
If player 2 is rational and I go to the ballgame, she should follow me there, and I’ll end up with a payoff of 6!”

41. Sequential rationality
Sequential rationality is when a player can count on the other players to behave rationally from that point forward
Similar to “dynamic consistency” (macro)
When an equilibrium satisfies sequential rationality, we call it a Subgame-Perfect Equilibrium
Players play best-responses both in the game as a whole, and in each “subgame,” or part of the game
Rules out the opera-opera equilibrium: in the subgame where P1 had already gone to the ballgame, P2 wasn’t playing a best-response
In fact, P2 only has one strategy that is sequentially rational: do whatever player 1 did!
also called “dynamic consistency” in macro - people make a plan at the beginning, but that plan still seems like the best available option when they reconsider it later, otherwise they wouldn’t stick to it

42. Subgame Perfect Equilibria are found by Backward Induction
PLAYER 1
Ballgame
Opera
PLAYER 2
PLAYER 2
Ballgame
Opera
Ballgame
Opera
(6, 3)
(0, 0)
(0, 0)
(3, 6)
Start at the “bottom,” solve for what P2 would do at each point
If P2 is rational and P1 knows it, P1 can infer what payoff he would get from each move
Now figure out what P1 would do, given those payoffs

43. Subgame Perfect Equilibria are found by Backward Induction
PLAYER 1
Ballgame
Opera
PLAYER 2
PLAYER 2
Ballgame
Opera
Ballgame
Opera
(6, 3)
(0, 0)
(0, 0)
(3, 6)
This game has a unique subgame-perfect equilibrium
Player 1 plays Ballgame
Player 2 plays Ballgame if 1 plays Ballgame, Opera if 1 plays Opera
“Most” dynamic games have just one SPE

44. Moving first can be good or bad, depending on the game
Battle of the sexes: moving first is good
You know your partner will accommodate whatever you do…
…so you get your first choice
Some games: being able to “commit” to a decision, while your opponent still has to decide, can be good!
(Another example: entry game)
Scissors-paper-rock: moving first is terrible
You always lose
Some games: reacting to your opponent’s move is good!

45. When we look at dynamic games, we’ll always look only at subgame-perfect equilibrium
Key assumption: common knowledge of rationality
Player 1 knows player 2 is rational…
…so whatever he does, she’ll do what’s best for her…
…so player 1 can confidently go to the ballgame
This is the key to sequential rationality
The assumption that, whatever happens first, players will continue to act rationally in their own best interest
Which means we can “solve the game” from the end, and figure out the beginning players’ optimal moves
(Backward induction has been used to solve checkers in 2007 – it’s a draw – and will eventually solve chess…)
The key assumption here is common knowledge of rationality
The players know each others’ payoff functions, everyone is rational, everyone knows everyone is rational, everyone knows everyone knows everyone is rational, and so on
If you’re playing a game like this against someone who’s crazy, it’s hard to know what would happen
And in fact, a “crazy” player – someone who doesn’t always do what’s best for them – might do better than a “rational” player
Because if I’m crazy and I’m firm 2, you might believe that I’ll actually fight if you enter; so you might choose not to enter
But if you know I’m rational, then you’re better off entering, since you know that once you enter, I won’t want to fight
(Literature on repeated games with reputation, where your actions in the early stages may partly be to try to convince opponents that you’re not a rational player, and therefore that they shouldn’t try to take advantage of you in later stages.)
But for us, we’ll stick to the assumption of rationality – I know that if I move first, my opponent will do whatever is in his best interest
This is referred to as sequential rationality – since the players are assumed to be rational at each stage of the game

46. Monday, we’ll start in on some particular applications of property law