Post on 14-Jan-2016
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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."
•
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.