Econ 521 - Week 12:
1. Infinitely Repeated Prisoner's Dilemma - Consider the following prisoner'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) Suppose now that players play G infinite times using grim trigger strategies. Is cooperating always (play (C, C) always) a SPNE? Is that cooperation sustainable? Consider each player's discount factor is δ.
2. Infinitely Repeated Game - Find the conditions on the discount factor under which cooperation can be supported in the infinitely repeated games with the following stage games.
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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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3,4
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0,7
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D
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5,0
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1,2
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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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3,2
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0,1
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D
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7,0
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2,1
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3. Interesting Question - Which is more important to achieve cooperation through a reputation in a game, a long history together or a long history ahead? Explain.
4. Infinitely Repeated Games II - Consider the following stage game,
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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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3,2
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0,1
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D
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7,0
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2,1
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(a) Under what conditions is there a subgame perfect equilibrium in which the players alternate between (C, C) and (C, D), starting with (C, C) in the first period? (use modified trigger strategies).
(b) Under what conditions is there a subgame perfect equilibrium in which the players alternate between (C, C) and (D, D), starting with (C, C) in the first period? (use modified trigger strategies).