Art Paintings Contracts by sfo41516

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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."
   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
  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.
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
  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.
      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.
  Holdup payoffs:(Buyer, Supplier)
                             Keep Price      (1000,0)
                                              Keep
Make investment     Supplier                  Supplier (250,750)
                          Raise price     Buyer
   Buyer
                                              New      (-500,-1000)
                                              Supplier
        Don’t invest
        (keep Supplier)     (0,0)
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.
      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.
 Holdup payoffs:(Buyer, Supplier)
                           Keep Price      (1000,0) (500,0)
                                            Keep
Make investment   Supplier                  Supplier (250,750)
                                                        (250,750)
                        Raise price     Buyer
  Buyer
                                            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
     made into a movie.
   – 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?
• 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)
                     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.
  – Need to assign intermediate nodes.
• May not work well if players care about
  fairness.

								
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