Econ 521 - Week 11:
1. Repeated Prisoner's Dilemma - Consider the following prisioner's dilemma game G
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2
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C
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D
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1
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C
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2,2
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0,3
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D
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3,0
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1,1
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(a) Solve for the Nash equilibrium of G.
(b) What if the game is repeated for two periods. Find the SPNE. Is cooperation (C, C) sustainable?
(c) Show that a finitely repeated Prisoner's Dilemma has a unique subgame perfect equilibrium, in which each player's strategy chooses D in every period, regardless of the history.
2. Another Prisoner's Dilemma - Consider the following prisioner's dilemma game G:
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2
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C
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D
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1
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C
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4,4
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-1,6
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D
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6,-1
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x,x
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Suppose x > 0.
(a) Solve for the Nash equilibrium of G.(b) What if the game is repeated for two periods. Find the SPNE. Is cooperation (C, C) sustainable for some value of x?
(c) What if the game is repeated T times? Is cooperation (C, C) sustainable?
3. Finitely Repeated Game - Consider a repeated game in which the stage game in the following stage game in the following figure is played in each of the two periods and there is no discounting.
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2
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L
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M
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R
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1
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U
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8,8
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0,9
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0,0
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C
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9,0
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0,0
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3,1
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D
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0,0
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1,3
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3,3
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(a) Is cooperation (U, L) sustainable in the first period? If so, show a strategy that sustain (U, L) in the first period.
(b) What can you conclude about cooperation/collusion in finitely repeated games?