# - Lecture 18 Assignment#4 due on Tuesday 22nd of March Innitely Repeated Prisoners Dilemma Recall 0 1 2 S 1/2 S = discount factor(0 S < 1 One-Shot

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** Assignment #4 due on Tuesday 22nd of March ** InFnitely Repeated Prisoners ʼ Dilemma: Recall: 0 1 2 S 1/2 S = discount factor (0 S < 1) One-Shot Prisoners ʼ Dilemma Player 2 Cooperate Defect Cooperate (2, 2) (0, 3) Player 1 Defect (3, 0) (1, 1) -Suppose that these two players have an arrangement, in which they each play opposite strategies, to come by higher payoffs: (C, D) (D, C) (C, D) (D, C) * * * * 0 1 2 3 (this is a crazy, very unrealistic, example, but it ʼ s being used to prove a point) -Now, if Player 1 is honest, and goes by the arrangement, then the Present Value Payoff (PVP) = = 0 + 3 δ + 0 + 3 δ 3 + 0 3 δ 5 + . .. = 3 δ (1 + δ 2 + δ 4 + . ..) = 3 δ / (1- δ 2 ) The PVP for cheating and not being honest is the following = 1 + δ + δ 2 + δ 3 + . .. = 1 / (1- δ ) So, in order to avoid any cheating: 3 δ / (1- δ 2 ) 1 / (1- δ ) 3 δ (1+ δ ) 2 δ 1 δ 1 / 2 Bertrand Equilibrium: (Special case of the Nash Equilibrium; one-shot game: firms choose prices as strategies) -Market: -2 firms selling IDENTICAL products (important that they be identical so only price matters) -Firms are prices setters -consumers pick firm with the lowest price 10 consumers Reservation Price = \$5 (max. consumer will pay) (each only wants 1 unit) Cost of Production = \$0 March 17, 2011 - Lecture 18

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- Lecture 18 Assignment#4 due on Tuesday 22nd of March Innitely Repeated Prisoners Dilemma Recall 0 1 2 S 1/2 S = discount factor(0 S < 1 One-Shot

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