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."

•

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.

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

Subgame perfection• A subgame is a point (node) where everyone

knows where they are.

• Say at every node, only one player makes a decision. 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.

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)

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)

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.

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 use the supplier.

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

Holdup payoffs:(Supplier, Buyer)

Buyer

Supplier

Keep Price

Raise price

Make investment

Don’t invest (keep Supplier) (0,0)

(0,1000)

(750,250)

Buyer

(-1000,-500)

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.

Holdup payoffs:(Supplier, Buyer)

Buyer

Supplier

Keep Price

Raise price

Make investment

Don’t invest (keep Supplier) (0,0)

(0,1000)

(750,250)

Buyer

(-1000,-500)

Keep Supplier

New Supplier

What if investment now costs 800?Potential savings 700. What happens?Another reason for a government to allow Vertical Integration.

(0,700)

(750,-50)

(-1000,-800)

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)

Frog

ScorpionCarry

Refuse

Sting

Refrain

(0,0)

(5,3)

(-10,5)

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

Incumbent

Entrant

Entrant

Enter

Exit

Enter

ExitExpandCapacity

Do nothing

(-10,5)

(0,20)

(0,15)

(10,10)

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?

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

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?

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:(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.

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)

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)

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.