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					A TYPE OF GAME
         Prisoner‟s Dilemma
     Classic example of a “game” devised at
         the RAND Corporation in 1950
 Two suspects are arrested for a crime in which
  they are both implicated. While separately
  interrogating them, the devious D.A. offers each
  one of them the same deal:
  • if only one of the two confesses, the squealer is
    released (payoff = 0) while the partner gets the
    maximum sentence of 10 years (payoff = -10)
  • if both confess, each one gets a medium sentence of 5
    years (payoff = -5)
  • if neither confesses, each gets two years (payoff = -2)
  MODELED AFTER
PRISONER‟S DILEMMA
             Cheater‟s Dilemma
          A “game” devised by the presenter
 Zany and Brainy are suspected of cheating on an
  exam. The professor asks to see both students in his
  office, but speaks to each one individually while the
  other “sweats it” outside. Anxious to get to the
  bottom of it, and knowing well that his students can
  never get enough points out of him, the crafty
  professor offers each student the same sweet deal:
 • if only one of you squeals, you get 50 points (payoff = +50)
  while your buddy forfeits 100 points (payoff = -100)
 • if you both end up squealing on each other, you each forfeit
  50 points (payoff = -50)
 • if neither one of you squeals, you each forfeit 25 points
  (payoff = -25)
         Payoff Matrix
             Brainy
            Squeal    Don’t
                      Squeal

Squeal    -50, -50 +50, -100
Don’t
Squeal    -100, +50 -25, -25
    Solution of “Game”
          Brainy
           Squeal    Don’t
                     Squeal

Squeal   -50, -50 +50, -100
Don’t
Squeal   -100, +50 -25, -25
        Repeated PD “Game”
 Includes finite repetition, infinite repetition, or
  games of unknown length.
 Players can now use prior knowledge when
  deciding on future moves.
 If players value long-term cooperation over short-
  term personal gain, the game may become
  cooperative over time (tacit pacts or even explicit
  enforceable agreements may be introduced)
 In a known finite number of iterations, the
  dilemma persists because when players know
  when the last move of the game will occur, they
  will always chose to defect (proof is inductive).
Computer Simulation Tournament
 Robert Axelrod* conducted a tournament of
  computer programs playing other computer
  programs with varying degrees of complexity.
 A four-line program submitted by
  mathematical psychologist, Anatol Rapoport,
  beat all others with the following simple
  instructions in a program called “Tit-for-Tat”:
  1. Start by choosing C.
  2. Thereafter, in each round, choose whatever
  your opponent chose in the previous round.
* Professor of Political Science & Public Policy at the University of Michigan
    Other Non-Zero-Sum “Games”
 Battle of the Sexes
Game has two pure strategy Nash Equilibria.
Named after the story concocted for this payoff structure by game
theorists in the „sexist‟ 1950s. A husband and wife were supposed
to choose between going to a boxing match or to a ballet and,
presumably for evolutionary genetic reasons, the husband preferred
„manly‟ boxing matches while the wife preferred „girly‟ ballets.

 Chicken
Game has pure strategy and mixed strategy Nash Equilibria.
Named after a teenage game popular in the 1950s. Two cars drive
straight toward each other at high velocity whereby the first driver
to swerve loses face.
Also used “as a metaphor for a situation where two parties engage
in a showdown where they have nothing to gain, and only pride
stops them from backing down.”
               Some History
 1940s: John von Neumann, Hungarian-born
  mathematician & Oskar Morgenstern, German-born
  Austrian economist, collaborated on the classic work,
  “Theory of Games and Economic Behavior”, upon
  which contemporary game theory is based.
 1950s: John Forbes Nash, Mathematics professor at
  Princeton and joint recipient of the1994 Nobel Prize
  in Economics, compiled and generalized prior results.
 1970s: John Maynard Smith, an English geneticist,
  applied game theory in biology; published “Evolution
  and the Theory of Games and Economic Behavior”.
 2005: Robert J. Aumann & Thomas C. Schelling,
  Israeli and American economists, received the Nobel
  Prize in Economics for their work on game theory.
        Specific Applications
    exist in any situation where we anticipate a
          rival‟s response to a given action
 ECONOMICS/BUSINESS: antitrust policy,
  pricing, marketing, auction rules, matching
  medical residents to hospital residency
  programs
 GOVERNMENT: election laws, nuclear
  deterrence policies
 SPORTS: coaching on running vs. passing vs.
  pitching fast balls vs. sliders
 BIOLOGY: identifying animal/plant species
  with greatest likelihood of extinction

				
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posted:9/2/2011
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