stolen art 50,000 paintings stolen from museums and private collections around the world (including...

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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."

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Page 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

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."

Page 2: 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

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.

Page 3: 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

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.

Page 4: 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

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 player’s possible decisions.

– At the end of the tree are the payoffs.

Page 5: 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

Graphing Extension Form games

A

B

a1

a2

b1

b1

b2

b2

(ua(a1,b2),ub(a1,b2))

(ua(a2,b2),ub(a2,b2))

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

(ua(a2,b1),ub(a2,b1))

B

B

A

Page 6: 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

Graphing Extension Form games

A

B

a1

a2

b1

b1

b2

b2

(ua(a1,b2),ub(a1,b2))

(ua(a2,b2),ub(a2,b2))

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

(ua(a2,b1),ub(a2,b1))

B

B

A

Players

Page 7: 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

Graphing Extension Form games

A

B

a1

a2

b1

b1

b2

b2

(ua(a1,b2),ub(a1,b2))

(ua(a2,b2),ub(a2,b2))

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

(ua(a2,b1),ub(a2,b1))

B

B

A

A’s decisions

Page 8: 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

Graphing Extension Form games

A

B

a1

a2

b1

b1

b2

b2

(ua(a1,b2),ub(a1,b2))

(ua(a2,b2),ub(a2,b2))

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

(ua(a2,b1),ub(a2,b1))

B

B

A

B’s decisions

Page 9: 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

Graphing Extension Form games

A

B

a1

a2

b1

b1

b2

b2

(ua(a1,b2),ub(a1,b2))

(ua(a2,b2),ub(a2,b2))

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

(ua(a2,b1),ub(a2,b1))

B

B

A

Payoffs

Page 10: 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

Stolen Art: Extension Form

A

B

Steal

Not Steal

Pay Fee

Don’t Pay

EnjoyThe art

(-20,-5)

(0,0)

(-10,5)

Museum

Thief

Museum

Page 11: 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

Stolen Art: Extension Form

A

B

Steal

Not Steal

Pay Fee

Don’t Pay

EnjoyThe art

(-20,-5)

(0,0)

(-10,5)

Museum

Thief

Museum

Players

Page 12: 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

Stolen Art: Extension Form

A

B

Steal

Not Steal

Pay Fee

Don’t Pay

EnjoyThe art

(-20,-5)

(0,0)

(-10,5)

Museum

Thief

Museum

Thief’s decisions

Page 13: 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

Stolen Art: Extension Form

A

B

Steal

Not Steal

Pay Fee

Don’t Pay

EnjoyThe art

(-20,-5)

(0,0)

(-10,5)

Museum

Thief

Museum

Museum’s decisions

Page 14: 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

A

B

Steal

Not Steal

Pay Fee

Don’t Pay

EnjoyThe art

(-20,-5)

(0,0)

(-10,5)

Museum

Thief

Museum

It costs the thief 5 to steal. (effort)

The fee=10.

The art is worth 20.

Page 15: 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

Ultimatum Game in Extensive Form

A

B

Offer(8,2)

Offer(5,5)

Accept

Accept

Reject

Reject

(0,0)

(0,0)

(8,2)

(5,5)

B

B

A

Page 16: 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

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.

Page 17: 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

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?

Page 18: 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

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.

Page 19: 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

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.

Page 20: 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

Bargaining w/ shrinking pie.

A

B

Offer(8,2)

Offer(5,5)

Accept

Accept

Reject

Reject

(2,4)

(5,5)

B

B

A

Size of £10 Size of £6

B

B

Offer(2,4)

Offer(3,3)

B

Accept

Accept

Reject

A

A

Reject (0,0)

(3,3)

(0,0)

(8,2)

Page 21: 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

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?

Page 22: 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

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.

Page 23: 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

Hold-up problem:(contractor, client)

Contractor

Client

Give In

Search Outside

High price

Normal price

(0,1300)

(1300,0)

(0,-100)

Note: High price is 1300 more than normal (competitive). Searching costs 1400.

Page 24: 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

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 supplier’s product.

• Once the investment is made, the supply can raise its prices.

Page 25: 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

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.

Page 26: 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

Holdup payoffs:(Buyer, Supplier)

Buyer

Supplier

Keep Price

Raise price

Make investment

Don’t invest (keep Supplier) (0,0)

(1000,0)

(250,750)

Buyer

(-500,-1000)

Keep Supplier

New Supplier

Buyer’s investment costs 500 – only useful for that supplier.Saves buyer 1500 (net 1000). Supplier can raise price by 750.Supplier losing the Buyer’s business costs him 1000.

Page 27: 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

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.

Page 28: 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

Holdup payoffs:(Buyer, Supplier)

Buyer

Supplier

Keep Price

Raise price

Make investment

Don’t invest (keep Supplier) (0,0)

(1000,0)

(250,750)

Buyer

(-500,-1000)

Keep Supplier

New Supplier

What if investment now costs 1000?Potential savings 500. What happens?Another reason for a government to allow Vertical Integration.

(500,0)

(250,750)

(-1000,-1000)

Page 29: 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

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.”

Page 30: 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

Frog and the Scorpion payoffs=(Frog,Scorpion)

Frog

ScorpionCarry

Refuse

Sting

Refrain

(0,0)

(5,3)

(-10,5)

Page 31: 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

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.

Page 32: 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

Simple Model of Entry Deterrence

Incumbent

Entrant

Entrant

Enter

Exit

Enter

ExitExpandCapacity

Do nothing

(-10,5)

(0,20)

(0,15)

(10,10)

Page 33: 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

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?

Page 34: 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

Patent Shelving(Incumbant, Entrant)

Incumbent

Entrant

Incumbent

Invest in patent

Do nothing

Invest in patent

Do nothing

(70,0)

(100,0)

(80,0)

(10,50)

Use

Shelve

Page 35: 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

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 didn’t USSR invade?

Page 36: 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

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?

Page 37: 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

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?

Page 38: 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

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.

Page 39: 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

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?

Page 40: 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

Kidnapping Game (parent, criminal, child)

Criminal

Don’t Kidnap

Kidnap Parent

Criminal

Exchange for Ransom

Don’t pay

Criminal

Kill

Release

(0,0,0)

(-3,10,-2)

(-10,-2,-20)

(-1,-5,-1)

Child

Identify

Refrain

(-1,-1,-3)

Page 41: 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

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.