mgf1107notes9

# mgf1107notes9 - Example Two persons accused of being...

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Example: Two persons accused of being partners in a crime are arrested and placed in separate cells so they cannot communicate with each other. Without a confession from one of the suspects, the district attorney has insufficient evidence to convict them of the crime. Both prisoners have the option of remaining silent or squealing on their partner. To extract a confession, the district attorney tells each suspect the following consequences of his and his partner’s actions. a) If one suspect confesses and his partner does not, the one who confesses can go free and the other gets a stiff 10-year sentence. b) If both suspects confess, they each get a reduced sentence of 5 years. c) If both suspects remain silent, they each go to jail for one year on a lesser charge. The payoff matrix is: Don’t confess Confess Don’t confess (-1, -1) (-10, 0) Confess (0, -10) (-5, -5) What is the best strategy for each prisoner? Solution: This is a famous problem in Game Theory, known as the Prisoner’s Dilemma. First note that this is not a zero-sum game. If one prisoner chooses to confess, his benefit (avoiding 10 years in prison) is not the other player’s loss. The ROW player has a dominant strategy, to confess. The same is true for the COLUMN player. Thus, when each prisoner strives to maximize his payoff independently, the pair is driven to the outcome (-5, -5). Note that this outcome also corresponds to the maximin strategy for each player. (We only have a minimax strategy for a column player in a zero-sum game.) The outcome (-1, -1), with better payoffs to both appears unobtainable when this game is played without cooperation. John Nash, a mathematician at Princeton University, shared the Nobel Prize in Economics in 1994 for his work in Game Theory. He is the subject of the movie A Beautiful Mind , starring Russell Crowe as Nash, which won the 2001 Oscar for Best Picture. Is (-5, -5) a Nash equilibrium? Can the ROW player

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mgf1107notes9 - Example Two persons accused of being...

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