Chapter13b

# Result cooperative outcome firm 2 p b p m firm1 p b

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Result: Cooperative outcome. Firm 2 P B P M Firm1 P B (1,1) (10-5=5,0+5=5) P M (0+5=5,10-5=5) (6,6)

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Duopoly - Revisited What if the penalty of 5 is not enforceable? Punishment imposed by the other firm. Tit-for-Tat: My action in this game depends on your action in the previous game. Grim Strategy: once a cheater always a cheater. Punishment sustains for the rest of the game. Consider the previous game with number of repetition (round) = 10. Firm 1 chooses to cooperate or not at round 10. If cooperate = 6 (and the other cooperates) If non-cooperate = 10 (and the other cooperates) Non-cooperate at round 10 for both firms. Move backward. Firm 1 chooses to cooperate or not at round 9 If cooperate = 6 + 0 = 6 Non cooperate = 10 + 0 = 10 Non-cooperate at round 9 and 10 for both firms. Keep moving backward and we will see that two firms will not cooperate in any of the round under grim strategy with 10 rounds. How to get a cooperative outcome?
Duopoly - Revisited Grim Strategy: once a cheater always a cheater. Punishment sustains for the rest of the game. Consider the previous game with number of repetition (round) = infinity. Firm 1 chooses to cooperate or not at round 1. If cooperate = 6 + 6 + 6 + 6 + … (and the other cooperates) If non-cooperate = 10 + 0 + 0 + 0 + … (and the other cooperates) Cooperate at round 1 for both firms. Move forward. Firm 1 chooses to cooperate or not at round 2 If cooperate = 6 + 6 + 6 + … = infinity Non cooperate = 10 + 0 + 0 + … = 10 Cooperate at round 1 and 2for both firms. Keep moving forward and we will see that two firms will always cooperate under grim strategy with infinity number of rounds.
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