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### plcy289_pset_8

Course: PLCY 289, Fall 2008
School: UNC
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Word Count: 254

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289 PLCY Problem Set 8 1. Consider the normal form stage game depicted in Figure 1. [Main result: If the stage game has only one NE, cooperation is not supported in the finite repeated game, but might be in the infinitely repeated game.] a. What is the equilibrium if this game is played only once? b. What is the equilibrium if this game is repeated 20 times? c. What is the highest discount factor (delta) which can...

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289 PLCY Problem Set 8 1. Consider the normal form stage game depicted in Figure 1. [Main result: If the stage game has only one NE, cooperation is not supported in the finite repeated game, but might be in the infinitely repeated game.] a. What is the equilibrium if this game is played only once? b. What is the equilibrium if this game is repeated 20 times? c. What is the highest discount factor (delta) which can sustain cooperation in the infinite version of this game? Figure 1 Player 2 Player 1 Deny Confess Deny 5,5 -5,10 Confess 10,-5 0,0 2. Professor B. Devil and his RA (a student of public policy) repeat the stage game depicted in Figure 2 three times with discounting. [Main result: Cooperation may be sustained in a finite game if there are NE multiple in the stage game.] a. Derive the pure strategy NE in the one-shot version of this game (ie. in the stage game). Is {Deny, Deny} a NE? b. In the game repeated 3 times, explain why {Deny, Deny} cannot be an equilibrium in all 3 periods. c. Describe a perfect equilibrium in which each person plays Deny in the first two periods. Explain why this equilibrium is sustainable. d. Suppose the stage game is only repeated twice. Is there a way ...

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