# Art Paintings Contracts by sfo41516

VIEWS: 5 PAGES: 41

Art Paintings Contracts document sample

• pg 1
Stolen Art
• 50,000 paintings stolen from museums and private
collections around the world (including 287 by Picasso, 43
by Van Gogh, 26 by Renoir, more than 100 by
Rembrandt).
• "Stolen art works don't end up on the walls of criminal
connoisseurs. They usually end up in storage.
• Mr Hill (former member of Metropolitan Police) : "I never
pay a ransom. What I do is settle expenses and provide a
finder's fee.“
• Tate Gallery paid 3 million pounds to someone who
engineered the return of 2 works by Turner.
• If thieves could somehow be persuaded that no finder's
fees would ever be paid, they might stop stealing works of
art. "But do you know a way to persuade them that no
collector, and no gallery, never mind an insurance
company, will ever hand over a cent to get its treasured
masterpieces returned?" he asks. "Because I don't."
Modeling with Game Theory
• What is the difference from previous “games” we
have studied?
– Decisions are made sequentially. (The thief decides
first.)
– Decisions of one player is seen by another player before
his decision is made. (If the thief steals, the museum
sees the art missing.)
• We can still use Game Theory to model the
previous problem.
• But first, let us play a game.
Ultimatum game
• One of you is Player A and the other is
Player B.
• You have £10 to divide between you.
• Player A makes an offer how to divide it to
Player B.
• Player B can accept or reject.
• If Player B accepts, the payoff is as offered.
If Player B rejects, they both get zero.
Extensive Form Games
(with perfect information)
• In both these games, decisions are made
sequentially with all players knowing fully what
• We can represent this problem by drawing a game
tree.
– Each node represents a player.
– Each branch represents a player’s possible decisions.
– At the end of the tree are the payoffs.
Graphing Extension Form games

b1        (ua(a1,b1),ub(a1,b1))

a1   B         b2
A
(ua(a1,b2),ub(a1,b2))
A
b1        (ua(a2,b1),ub(a2,b1))
a2
B
B

b2          (ua(a2,b2),ub(a2,b2))
Graphing Extension Form games
Players
b1        (ua(a1,b1),ub(a1,b1))

a1   B         b2
A
(ua(a1,b2),ub(a1,b2))
A
b1        (ua(a2,b1),ub(a2,b1))
a2
B
B

b2          (ua(a2,b2),ub(a2,b2))
Graphing Extension Form games
A’s decisions
b1        (ua(a1,b1),ub(a1,b1))

a1        B         b2
A
(ua(a1,b2),ub(a1,b2))
A
b1        (ua(a2,b1),ub(a2,b1))
a2
B
B

b2          (ua(a2,b2),ub(a2,b2))
Graphing Extension Form games
B’s decisions
b1        (ua(a1,b1),ub(a1,b1))

a1     B         b2
A
(ua(a1,b2),ub(a1,b2))
A
b1        (ua(a2,b1),ub(a2,b1))
a2
B
B

b2          (ua(a2,b2),ub(a2,b2))
Graphing Extension Form games
Payoffs

b1        (ua(a1,b1),ub(a1,b1))

a1   B         b2
A
(ua(a1,b2),ub(a1,b2))
A
b1        (ua(a2,b1),ub(a2,b1))
a2
B
B

b2          (ua(a2,b2),ub(a2,b2))
Stolen Art: Extension Form

Pay Fee    (-10,5)

Steal Museum Don’t Pay

A
(-20,-5)
Thief
Not Steal
B
Museum

Enjoy          (0,0)
The art
Stolen Art: Extension Form
Players
Pay Fee    (-10,5)

Steal Museum Don’t Pay

A
(-20,-5)
Thief
Not Steal
B
Museum

Enjoy          (0,0)
The art
Stolen Art: Extension Form
Thief’s decisions
Pay Fee    (-10,5)

Steal Museum Don’t Pay

A
(-20,-5)
Thief
Not Steal
B
Museum

Enjoy          (0,0)
The art
Stolen Art: Extension Form
Museum’s decisions
Pay Fee    (-10,5)

Steal Museum Don’t Pay

A
(-20,-5)
Thief
Not Steal
B
Museum

Enjoy          (0,0)
The art
It costs the thief 5 to steal.
(effort)
The fee=10.
The art is worth 20.
Pay Fee    (-10,5)

Steal Museum Don’t Pay

A
(-20,-5)
Thief
Not Steal
B
Museum

Enjoy          (0,0)
The art
Ultimatum Game in Extensive
Form
Accept      (8,2)

Offer
(8,2)   B
Reject
A                               (0,0)
A
Accept      (5,5)
Offer
(5,5)    B
B

Reject        (0,0)
Subgame perfection
• These games are called extensive form games
with perfect information.
• A set of strategies is a subgame perfect
equilibrium if at every node (including those
never reached), a player chooses his optimal
strategy knowing that every node in the future
the same will happen.
Backward Induction
• To solve for the subgame perfect equilibria, one
can start at the end nodes.
• Determine what are the decisions at the end.
• Replace other earlier branches with the payoffs.
• Repeat.

• What are the subgame perfect equilibria in the
ultimatum game?
• If players are irrational at nodes not reached, can a
player rationally choose a strategy that isn’t the
subgame perfect strategy?
Gender in Ultimatum games
(Solnick 2001)
• Male offers to males \$4.73> to females
\$4.43
• Female offers to males \$5.13> to females
\$4.31.
• Males accept \$2.45 from other males<\$2.82
from females.
• Females accept \$3.39 from males<\$4.15
from females.
Bargaining w/ shrinking pie
• Take the ultimatum game. Assume when
there is a rejection the responder can make a
counter-proposal.
• However, the pie shrinks after a rejection.
• What is the subgame perfect equilibrium
when the pie shrinks from £10 to £6.
Bargaining w/ shrinking pie.
Size of £10                             Size of £6

Accept (8,2)
Offer          Accept (2,4)
Offer                           (2,4)
(8,2)    B                                A
Reject
A                                B                   Reject   (0,0)
A
Accept   (5,5)                  Accept (3,3)
Offer
(5,5)    B
B                             B
Offer A
(3,3)
Reject       B                  Reject    (0,0)
Bargaining Discussion
• Do pies really shrink?
• The main government labour union in Israel
went on strike in September shutting down
most of the country.
• From our analysis why do strikes happen?
Hold-up problem
• A Contractor is hired to construct a building.
• Unexpected need emerges (new colour).
• Contractor can charge cost of change or high
price.
• Client can agree or try to find outside help.
• Client is held up.
• Can one “solve” this with more explicit contracts?
• Reputation effects.
Hold-up problem:
(contractor, client)
Give In   (1300,0)

High price     Client

Search        (0,-100)
Contractor                       Outside
Normal price

(0,1300)

Note: High price is 1300 more than normal (competitive).
Searching costs 1400.
Supplier hold-up problem
• If one company is supplying another company a
good used in production (such as a supplier of coal
to an electric company), then the supplier can
• This works if the buyer company decides to make
an investment to adjust its products to make better
use of the supplier’s product.
• Once the investment is made, the supply can raise
its prices.
Supplier hold-up problem
• The investment by the buyer costs him 500.
• The gross gain to the buyer is 1500.
• The net gain is 1500-500=1000.
• The supplier can raise the price by 750
• This would reduce the net gain of the buyer by
750 to 250.
• If the buyer switches to a new supplier, the
buyer’s investment (of 500) is lost to him and the
supplier loses 1000 worth of previous business
with him.
Keep Price      (1000,0)
Keep
Make investment     Supplier                  Supplier (250,750)
New      (-500,-1000)
Supplier
Don’t invest
(keep Supplier)     (0,0)
Buyer’s investment costs 500 – only useful for that supplier.
Supplier can raise price by 750.
Supplier hold-up problem
• Now the investment is 1000 (instead of 500).
• The gross gain to the buyer remains 1500.
• The net gain changes to 1500-1000=500.
• The supplier can still raise the price by 750
• This would reduce the net gain of the buyer by
750 to -250. (rather than +250)
• If the buyer switches to a new supplier, the
buyer’s investment (of 1000) is lost to him and the
supplier loses 1000 worth of previous business
with him.
Keep Price      (1000,0) (500,0)
Keep
Make investment   Supplier                  Supplier (250,750)
(250,750)
New      (-500,-1000)
Supplier
(-1000,-1000)
Don’t invest
(keep Supplier)     (0,0)
What if investment now costs 1000?
Potential savings 500. What happens?
Another reason for a government to allow Vertical Integration.
Frog and the Scorpion
• Frog and Scorpion were at the edge of a river
wanting to cross.
• The Scorpion said “I will climb on you back and
you can swim across.”
• Frog said “But what if you sting me.”
• Scorpion answered, “Why would I do that? Then
we both die.”
• What happened?
• Scorpion stung. The frog who cried “Now we are
both doomed! Why did you do that?”
• “Alas,” said the Scorpion, “it is my nature.”
Frog and the Scorpion
payoffs=(Frog,Scorpion)

Sting     (-10,5)

Scorpion
Carry
Refrain
(5,3)
Frog
Refuse

(0,0)
Simple Model of Entry Deterrence
• A incumbent monopolist controls a market.
• A potential entrant is thinking of entering.
• The incumbent can expand capacity (or
invest in a new technology) that is costly
and not needed unless the entrant enters.
• The entrant is deterred by this and stays out.
Simple Model of Entry Deterrence
Enter    (-10,5)

Expand     Entrant    Exit
Capacity                      (0,15)

Incumbent                        Enter   (10,10)

Entrant
Do nothing
Exit    (0,20)
Patent Shelving
• Other deterrents to entry: patent shelving – throw
the innovation in the closet.
• Incumbant can invest in a patent. While the
technology may be better than the current that it
uses, it may be too expensive to adapt existing
product line. Why?
• Case studies
– Lucent buys Chromatis for \$4.8 billion never uses
product. Lucent wants to prevent Nortel from buying it.
– Hollywood: Top screen writers may rarely see a script
– Microsoft: Does it really take hundreds of programmers
to write word?
Patent Shelving
(Incumbant, Entrant)
Use         (70,0)

Incumbent
Invest in patent               Shelve
(80,0)

Incumbent                     Invest in patent (10,50)

Entrant
Do nothing
Do         (100,0)
nothing
War Games
• Cold War Strategy: MAD, mutually assured
destruction. Both the US and USSR had enough
nuclear weapons to destroy each other.
• What does the game tree look like?
• The US put troops in Germany and said that if
West German were attacked it would mean
nuclear war.
• Would this have happened?
New War Games
• Israel and Iran.
– Israel is a nuclear power and Iran is close to becoming
one. Will Israel attack Iran like they did Iraq?
– Iran warns Israel that an attack will mean a harsh
response. Is this credible?
– Why would Israel not want a MAD situation?
– Could it make sense for missile defence rather than
offensive attack.
– The Israeli spy satellite Ofek 6 malfunctioned and was
destroyed on launch. This may make a window where
Israel will be blind. How may this increase the chance
of an attack?
New War Games
• US and North Korea.
– North Korea is manufacturing a bomb.
– US is threatening an attack.
– US has troops in North Korea. Bush is
considering reducing the numbers. Why?
Bible Games:

whether or not to eat the
forbidden fruit from the
tree of knowledge.

If they eat, God knows
and decides upon a
punishment.
Kidnapping Game
•   Criminal Kidnaps Teen.
•   Requests ransom and threatens to kill if not paid.
•   Parent decides whether or not to pay.
•   If parent does not pay, criminal decides whether or
not to kill hostage.
•   Start at end. Does the criminal kill if no ransom is
paid?
•   What happens if there is no way to exchange
ransom?
•   How can the hostage save himself if no ransom is
paid?
•   What should a country do if its citizens are held
for ransom?
Kidnapping Game
(parent, criminal, child)
Exchange for Ransom
(-3,10,-2)

(-10,-2,-20)
Kidnap Parent       Don’t pay        Kill
Criminal                      Criminal              Identify (-1,-5,-1)
Release
Child
Don’t Kidnap (0,0,0)                              Refrain
(-1,-1,-3)
How reasonable is backward
induction?
• May work in some simple games.
• Tic Tac Toe, yes, but how about Chess?
– Too large of a tree.