Stolen Art

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."

2
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.

3
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.

4
Extensive Form Games (with perfect information)

• In both these games, decisions are made
  sequentially with all players knowing fully what
  the decisions were made prior.
• We can represent this problem by drawing a game
  tree.
• Each node represents a player.
• Each branch represents a players possible
  decisions.
• At the end of the tree are the payoffs.

5
Graphing Extension Form games
(ua(a1,b1),ub(a1,b1))
b1
a1
B
b2
(ua(a1,b2),ub(a1,b2))
A
A
(ua(a2,b1),ub(a2,b1))
b1
a2
B
B
(ua(a2,b2),ub(a2,b2))
b2
6
Graphing Extension Form games
Players
(ua(a1,b1),ub(a1,b1))
b1
a1
B
b2
(ua(a1,b2),ub(a1,b2))
A
A
(ua(a2,b1),ub(a2,b1))
b1
a2
B
B
(ua(a2,b2),ub(a2,b2))
b2
7
Graphing Extension Form games
As decisions
(ua(a1,b1),ub(a1,b1))
b1
a1
B
b2
(ua(a1,b2),ub(a1,b2))
A
A
(ua(a2,b1),ub(a2,b1))
b1
a2
B
B
(ua(a2,b2),ub(a2,b2))
b2
8
Graphing Extension Form games
Bs decisions
(ua(a1,b1),ub(a1,b1))
b1
a1
B
b2
(ua(a1,b2),ub(a1,b2))
A
A
(ua(a2,b1),ub(a2,b1))
b1
a2
B
B
(ua(a2,b2),ub(a2,b2))
b2
9
Graphing Extension Form games
Payoffs
(ua(a1,b1),ub(a1,b1))
b1
a1
B
b2
(ua(a1,b2),ub(a1,b2))
A
A
(ua(a2,b1),ub(a2,b1))
b1
a2
B
B
(ua(a2,b2),ub(a2,b2))
b2
10
Stolen Art Extension Form
(-10,5)
Pay Fee
Steal
Museum
Dont Pay
(-20,-5)
A
Thief
Not Steal
B
Museum
(0,0)
Enjoy The art
11
Stolen Art Extension Form
Players
(-10,5)
Pay Fee
Steal
Museum
Dont Pay
(-20,-5)
A
Thief
Not Steal
B
Museum
(0,0)
Enjoy The art
12
Stolen Art Extension Form
Thiefs decisions
(-10,5)
Pay Fee
Steal
Museum
Dont Pay
(-20,-5)
A
Thief
Not Steal
B
Museum
(0,0)
Enjoy The art
13
Stolen Art Extension Form
Museums decisions
(-10,5)
Pay Fee
Steal
Museum
Dont Pay
(-20,-5)
A
Thief
Not Steal
B
Museum
(0,0)
Enjoy The art
14
It costs the thief 5 to steal. (effort) The
fee10. The art is worth 20.
(-10,5)
Pay Fee
Steal
Museum
Dont Pay
(-20,-5)
A
Thief
Not Steal
B
Museum
(0,0)
Enjoy The art
15
Ultimatum Game in Extensive Form
(8,2)
Accept
Offer (8,2)
B
Reject
(0,0)
A
A
Accept
(5,5)
Offer (5,5)
B
B
(0,0)
Reject
16
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.

17
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
  isnt the subgame perfect strategy?

18
Gender in Ultimatum games(Solnick 2001)

• Male offers to males 4.73gt to females 4.43
• Female offers to males 5.13gt to females 4.31.
• Males accept 2.45 from other maleslt2.82 from
  females.
• Females accept 3.39 from maleslt4.15 from
  females.

19
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.

20
Bargaining w/ shrinking pie.
Size of 10
Size of 6
Accept
(8,2)
Accept
Offer (2,4)
(2,4)
Offer (8,2)
B
A
Reject
Reject
(0,0)
B
A
A
Accept
Accept
(5,5)
(3,3)
Offer (5,5)
B
B
B
A
Offer (3,3)
B
(0,0)
Reject
Reject
21
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?

22
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.

23
Note High price is 1300 more than normal
(competitive). Searching costs 1400.
24
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 hold-up the buyer company.
• This works if the buyer company decides to make
  an investment to adjust its products to make
  better use of the suppliers product.
• Once the investment is made, the supply can raise
  its prices.

25
Supplier hold-up problem

• The investment by the buyer costs him 500.
• The gross gain to the buyer is 1500.
• The net gain is 1500-5001000.
• 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
  buyers investment (of 500) is lost to him and
  the supplier loses 1000 worth of previous
  business with him.

26
Holdup payoffs(Buyer, Supplier)
Keep Price
(1000,0)
Keep Supplier
Make investment
Supplier
(250,750)
Raise price
Buyer
Buyer
(-500,-1000)
New Supplier
Dont invest (keep Supplier)
(0,0)
Buyers investment costs 500 only useful for
that supplier. Saves buyer 1500 (net 1000).
Supplier can raise price by 750. Supplier losing
the Buyers business costs him 1000.
27
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 1500-1000500.
• 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
  buyers investment (of 1000) is lost to him and
  the supplier loses 1000 worth of previous
  business with him.

28
Holdup payoffs(Buyer, Supplier)
Keep Price
(1000,0)
(500,0)
Keep Supplier
Make investment
Supplier
(250,750)
(250,750)
Raise price
Buyer
Buyer
(-500,-1000)
New Supplier
(-1000,-1000)
Dont 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.
29
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.

30
Frog and the Scorpion payoffs(Frog,Scorpion)
Sting
(-10,5)
Scorpion
Carry
Refrain
(5,3)
Frog
Refuse
(0,0)
31
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.

32
Simple Model of Entry Deterrence
Enter
(-10,5)
Entrant
Exit
Expand Capacity
(0,15)
Incumbent
(10,10)
Enter
Entrant
Do nothing
(0,20)
Exit
33
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 made into a movie.
• Microsoft Does it really take hundreds of
  programmers to write word?

34
Patent Shelving (Incumbant, Entrant)
(70,0)
Use
Incumbent
Shelve
Invest in patent
(80,0)
Incumbent
Invest in patent
(10,50)
Entrant
Do nothing
(100,0)
Do nothing
35
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?
• Why didnt USSR invade?

36
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?

37
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?

38
Bible Games (Adam Eve, God) Adam and Eve
decide whether or not to eat the forbidden fruit
from the tree of knowledge. If they eat, God
knows and decides upon a punishment.
39
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?

40
Kidnapping Game (parent, criminal, child)
Exchange for Ransom
(-3,10,-2)
(-10,-2,-20)
Parent
Dont pay
Kidnap
Kill
Criminal
Criminal
Criminal
(-1,-5,-1)
Identify
Release
Child
Refrain
Dont Kidnap
(0,0,0)
(-1,-1,-3)
41
How reasonable is backward induction?

• May work in some simple games.
• Tic Tac Toe, yes, but how about Chess?
• Too large of a tree.
• Need to assign intermediate nodes.
• May not work well if players care about fairness.