Econ 522
Economics of Law
Dan Quint
Fall 2009
Lecture 3
Tuesday, we discussed efficiency
 efficiency: “when there is no way to make some people in the
economy better off, without making others worse off by more”
 saw some examples of forces that lead to inefficiency

externalities; barriers to trade; monopoly/private information; taxes
 considered limitations of efficiency

doesn’t address equity/distribution; assumes value = willingness to pay
(everything is monetizable); only considers outcomes, not process
 saw two arguments why the law should be designed to be efficient

Posner: ex-ante consent
 Cooter/Ulen: if we’re worried about distribution/equity, better to design the
law to be efficient, use tax system to redistribute wealth
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Today:
 introduce some basic game theory
 begin property law
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But first, a quick digression…
 I don’t have many “absolute beliefs” about economics

Some people do
 I hope that doesn’t make things too confusing
 Relatedly, if I don’t see economics as a set of rules to
memorize, how do I know what I know?

I need to see a model, or an example, that demonstrates it
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Some basic
game theory
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A brief introduction to game theory
 Today, we focus on static games

Also known as simultaneous-move games
 A static game is completely described by three things:



Who the players are
What actions are available to each player
What payoff each player will get, as a function of


his own action, and
the actions of the other players
 Any complete description of these three things fully
characterizes a static game
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A classic example: the Prisoner’s Dilemma
 (Story)
 Players: player 1 and player 2
 Two actions available to each player: rat on the other, or
keep mum
 Payoffs:





u1(mum, mum) = -1
u1(rat, mum) = 0
u1(mum, rat) = -10
u1(rat,rat) = -5
Same for player 2
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In two-player games with finite actions, one
way to present game is payoff matrix
Player 2’s Action
Always Player 1
Mum
Rat
Mum
-1, -1
-10, 0
Rat
0, -10
-5, -5
Player 1’s Action
Player 1’s Payoff
Player 2’s Payoff
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Dominant Strategies
 In the Prisoner’s Dilemma, one player’s best action is the
same, regardless of what his opponent does
Player 1’s Action
Player 2’s Action
Mum
Rat
Mum
-1, -1
-10, 0
Rat
0, -10
-5, -5
 This is called a dominant strategy

Regardless of what he thinks 2 will do, 1 will choose to play Rat
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Nash Equilibrium
 In most games, players won’t have a single move that’s
always best
 We solve a game by looking for a Nash equilibrium
 Nash equilibrium is a strategy profile (an action for each
player) such that:


No player can improve his payoff by switching to a different action…
Given what his opponent/opponents are doing
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A strategy profile is a Nash Equilibrium if no
player can gain by deviating
 Is (Mum, Mum) an equilibrium?
No, if player 2 is playing Mum
player 1 gains by deviating
 If any player can improve
his payoff by changing his
action, given his opponents’
actions, then it is not a Nash
equilibrium
Player 2’s Action
Player 1’s Action

Mum
Rat
Mum
-1, -1
-10, 0
Rat
0, -10
-5, -5
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In two-player games, we find Nash equilibria
by highlighting best responses
 Given a possible action by my opponent, my best response
is whatever action(s) give me the highest payoff
Player 2’s Action



Circle payoff from player 1’s
best response to each action
by his opponent
Circle payoff from player 2’s
best response to each action
Any box with both payoffs
circled is an equilibrium
Player 1’s Action
 To find Nash Equilibria…
Mum
Rat
Mum
Rat
-1, -1
-10, 0
0, -10
-5, -5
 In the Prisoner’s Dilemma game, (Rat, Rat), or “Both players
play Rat”, is the only Nash equilibrium
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Some games will have more than one
equilibrium
 Another classic: Battle of the Sexes
 (Story)
 Circle player 2’s
best responses
 We find two equilibria:
(ballgame, ballgame)
and (opera, opera)

Player 1’s Action
 Circle player 1’s
best responses
Player 2’s Action
Baseball Game
Opera
Baseball
Game
6, 3
0, 0
Opera
0, 0
3, 6
Game theory usually doesn’t have that much to say about which
equilibrium will get played when there are more than one
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Sometimes, there will be a “good” and a
“bad” equilibrium
 Growth model
 (Story)
 Circle player 2’s
best responses
 Two equilibria:
(invest, invest)
and (consume, consume)

Player 1’s Action
 Circle player 1’s
best responses
Player 2’s Action
Invest
Consume
Invest
2, 2
0, 1
Consume
1, 0
1, 1
Some papers explain differences in growth across countries by
saying some are in “good” equilibrium and some are in “bad” one
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Some games don’t have any equilibrium
where players only play one action



Look for Nash
Equilibria by
circling best
responses
No square with
both payoffs
circled
No equilibrium
where each
player plays a
single action
Player 1’s Action
 Scissors, Paper, Rock for $1
Player 2’s Action
Scissors
Paper
Rock
Scissors
0, 0
1, -1
-1, 1
Paper
-1, 1
0, 0
1, -1
Rock
1, -1
-1, 1
0, 0
 In this class, we’ll focus on games with a pure-strategy
Nash equilibrium
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That’s a very quick introduction to static
games
 Now on to…
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Property Law
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Why do we need property law at all?
 In a sense, same question as,
why do we prefer organized society of any sort to anarchy?
 Suppose there are two neighboring farmers
 Each can either farm his own land, or steal crops from his
neighbor

Stealing is probably less efficient than planting my own crops




Have to carry the crops from your land to mine
Might drop some along the way
Have to steal at night  move slower
If I steal your crops, I avoid the effort of planting and watering
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Why do we need property law?
 Suppose that planting and watering costs 5, the crops either
farmer could grow are worth 15, and stealing costs 3
 With no legal system,
the game has the
following payoffs:
 We look for equilibrium
Player 1
Player 2
Farm
Steal
Farm
10, 10
-5, 12
Steal
12, -5
0, 0
 Like Prisoner’s Dilemma


both farmers stealing is the only equilibrium
but that outcome is Pareto-dominated by both farmers farming
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So how do we fix the problem?
 Suppose there were lots of farmers facing this same
problem
 They come up with an idea:


Institute some property rights
And some type of government that would punish people who steal
 Setting up the system would cost something

Suppose it imposes a cost c on everyone who plays by the rules
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ORIGINAL GAME
MODIFIED GAME
Player 2
Player 2
Farm
Steal
Farm
10, 10
-5, 12
Steal
12, -5
0, 0
Farm
Player 1
Player 1
So how do we fix the problem?
Steal
Farm 10 – c, 10 – c -5 – c, 12 – P
Steal 12 – P, -5 – c
-P, -P
 If P is big, and c is not too big, then 12 – P < 10 – c
 In that case, (Farm, Farm) is an equilibrium

Payoffs are (10 – c, 10 – c), instead of (0, 0) from before
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So the idea here…
 Anarchy is inefficient



I spend time and effort stealing from you
You spend time and effort defending your property from thieves
Instead of doing productive work
 Establishing property rights, and a legal process for when
they’re violated, is one way around the problem
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Overview of Property Law
 Cooter and Ulen: property is
“A bundle of legal rights over resources that the owner is free to
exercise and whose exercise is protected from interference by others”
 Property rights are not absolute

Appendix to ch. 4 discusses different conceptions of property rights
 Any system has to answer four fundamental questions:




What things can be privately owned?
What can (and can’t) an owner do with his property?
How are property rights established?
What remedies are given when property rights are violated?
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Answers to many of these seem obvious
 BUT…
 http://www.msnbc.msn.com/id/21088150/
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One early, “classic” property law case
 Pierson v. Post (NY Supreme Court, 1805)




Post organized a fox hunt, was chasing a fox
Pierson appeared “out of nowhere,” killed the fox, took it
Post sued to get the fox back
Lower court sided with Post; Pierson appealed to NY Sup Ct

Both were wealthy, pursued the case on principle or out of spite
 Question: when do you own an animal?
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Pierson v. Post
 Court ruled for Pierson (the one who killed the fox)


“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”
(Also: just because an action is “uncourteous or unkind” does not
make it illegal)
 Dissenting opinion: a fox is a “wild and noxious beast,” and
killing foxes is “meritorious and of public benefit”

Post should own the fox, in order to encourage fox hunting
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Same tradeoff we saw earlier:
Pierson gets the fox

simpler rule (finders
keepers)

easier to implement

fewer disputes
Post gets the fox

more efficient incentives

(stronger incentive to pursue
animals that may be hard to
catch)
 Just like Fast Fish/Loose Fish vs Iron Holds The Whale


Fast Fish/Loose Fish is the simpler rule, leads to fewer disputes
Iron Holds the Whale is more complicated, but is necessary with
whales where huting them the old-fashioned way is too dangerous
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Next up:
Coase
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The Coase Theorem
 Ronald Coase (1960), “The Problem of Social Cost”
 In the absence of transaction costs,
if property rights are well-defined
and tradeable, voluntary negotiations
will lead to efficiency.

So the initial allocation of rights
doesn’t matter for efficiency

However, it does matter for distribution

And if there are transaction costs,
it may matter for efficiency too
An example of the Coase Theorem
 Your car – worth $3,000 to you, $4,000 to me
 The key: lack of transaction costs
Coase
 “In the absence of transaction costs, if property rights are
well-defined and tradeable, voluntary negotiations will lead
to efficiency”
Example from Coase – a rancher and a
farmer
Example from Coase – a rancher and a
farmer
Other examples from Coase
 Lots of examples from case law





a building that blocked air currents from turning a windmill
a building which cast a shadow over the swimming pool and
sunbathing area of a hotel next door
a doctor next door to a confectioner
a chemical manufacturer
a house whose chimney no longer worked well after the neighbors
rebuilt their house to be taller
 In each case, regardless of who is initially held liable, the
parties can negotiate with each other and take whichever
remedy is cheapest to fix (or endure) the situation
Quoting from Coase (p. 13):
Judges have to decide on legal liability but this should not
confuse economists about the nature of the economic
problem involved.
In the case of the cattle and the crops, it is true that there
would be no crop damage without the cattle. It is equally
true that there would be no crop damage without the crops.
The doctor’s work would not have been disturbed if the
confectioner had not worked his machinery; but the
machinery would have disturbed no one if the doctor had
not set up his consulting room in that particular place…
Quoting from Coase (p. 13):
If we are to discuss the problem in terms of causation, both
parties cause the damage.
If we are to attain an optimum allocation of resources, it is
therefore desireable that both parties should take the
harmful effects into account when deciding on their course
of action.
It is one of the beauties of a smoothly operating pricing
system that… the fall in the value of production due to the
harmful effect would be a cost for both parties.
Tuesday: transaction costs
 Please see me if you’re not yet registered
 Take a look at Coase and Demsetz papers
 Have a good weekend
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