Econ 522 Economics of Law

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Econ 522Economics of Law
Dan Quint Fall 2009 Lecture 3
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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
• doesnt 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 were 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 dont have many absolute beliefs about
  economics
• Some people do
• I hope that doesnt make things too confusing
• Relatedly, if I dont 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 basicgame 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 Prisoners 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 2s Action
Always Player 1
Mum
Rat
-1, -1
-10, 0
Mum
Player 1s Action
0, -10
-5, -5
Rat
Player 1s Payoff
Player 2s Payoff
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Dominant Strategies

• In the Prisoners Dilemma, one players best
  action is the same, regardless of what his
  opponent does
• This is called a dominant strategy
• Regardless of what he thinks 2 will do, 1 will
  choose to play Rat

Player 2s Action
Mum
Rat
-1, -1
-10, 0
Mum
Player 1s Action
0, -10
-5, -5
Rat
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Nash Equilibrium

• In most games, players wont have a single move
  thats 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 Mumplayer 1 gains by
  deviating
• If any player can improvehis payoff by changing
  hisaction, given his opponentsactions, then it
  is not a Nashequilibrium

Player 2s Action
Mum
Rat
-1, -1
-10, 0
Mum
Player 1s Action
0, -10
-5, -5
Rat
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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
• To find Nash Equilibria
• Circle payoff from player 1sbest response to
  each action by his opponent
• Circle payoff from player 2sbest response to
  each action
• Any box with both payoffscircled is an
  equilibrium
• In the Prisoners Dilemma game, (Rat, Rat), or
  Both players play Rat, is the only Nash
  equilibrium

Player 2s Action
Mum
Rat
-1, -1
-10, 0
Mum
Player 1s Action
0, -10
-5, -5
Rat
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Some games will have more than one equilibrium

• Another classic Battle of the Sexes
• (Story)
• Circle player 1sbest responses
• Circle player 2sbest responses
• We find two equilibria (ballgame, ballgame)
  and (opera, opera)
• Game theory usually doesnt have that much to say
  about which equilibrium will get played when
  there are more than one

Player 2s Action
Baseball Game
Opera
6, 3
0, 0
BaseballGame
Player 1s Action
0, 0
3, 6
Opera
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Sometimes, there will be a good and a bad
equilibrium

• Growth model
• (Story)
• Circle player 1sbest responses
• Circle player 2sbest responses
• Two equilibria (invest, invest)and (consume,
  consume)
• Some papers explain differences in growth across
  countries by saying some are in good
  equilibrium and some are in bad one

Player 2s Action
Invest
Consume
2, 2
0, 1
Invest
Player 1s Action
1, 0
1, 1
Consume
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Some games dont have any equilibrium where
players only play one action

• Scissors, Paper, Rock for 1
• Look for Nash Equilibria by circling best
  responses
• No square with both payoffs circled
• No equilibrium where each player plays a
  single action
• In this class, well focus on games with a
  pure-strategyNash equilibrium

Player 2s Action
Scissors
Paper
Rock
0, 0
1, -1
-1, 1
Scissors
-1, 1
0, 0
1, -1
Paper
Player 1s Action
1, -1
-1, 1
0, 0
Rock
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Thats 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
• Like Prisoners Dilemma
• both farmers stealing is the only equilibrium
• but that outcome is Pareto-dominated by both
  farmers farming

Player 2
Farm
Steal
10, 10
-5, 12
Farm
Player 1
12, -5
0, 0
Steal
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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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So how do we fix the problem?
MODIFIED GAME
ORIGINAL GAME
Player 2
Player 2
Farm
Steal
Farm
Steal
10, 10
-5, 12
10 c, 10 c
-5 c, 12 P
Farm
Farm
Player 1
Player 1
12 P, -5 c
-P, -P
12, -5
0, 0
Steal
Steal

• If P is big, and c is not too big, then 12 P lt
  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 theyre 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 cant) 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 doesnt
  matter for efficiency
• However, it does matter for distribution
• And if there are transaction costs, it may
  matter for efficiency too

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An example of the Coase Theorem

• Your car worth 3,000 to you, 4,000 to me
• The key lack of transaction costs

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Coase

• In the absence of transaction costs, if property
  rights are well-defined and tradeable, voluntary
  negotiations will lead to efficiency

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Example from Coase a rancher and a farmer
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Example from Coase a rancher and a farmer
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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

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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 doctors 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
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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.
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Tuesday transaction costs

• Please see me if youre not yet registered
• Take a look at Coase and Demsetz papers
• Have a good weekend