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Repeated Games and the Prisoner’s Dilemma

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Prisoner’s dilemma What if the game is played “repeatedly” for several periods? DefectCooperate Defect10 yr, 10 yr1 yr, 25 yr Cooperate25 yr, 1 yr3 yr, 3 yr

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Tainan Hotel and Shangri-La Hotel For a cooperative agreement 3 or more months, to defect seems not profitable for each player. How should player react seeing this fact? AggressivePeaceful Aggressive200, , 100 Peaceful100, , 250

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Finite repetition Games where two players play the same game for a certain finite periods. Rollback equilibrium → Each will defect from the very last period back to the first period. This result holds for known finite periods of time.

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Infinite Repetition If the same interaction will continue for infinite periods, without ending? Contingent strategies/trigger strategies Grim strategy Tit-for-tat (TFT)

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Options for Tainan Hotel other than playing cooperatively all the time (assuming Shangri-la playing TFT is common knowledge ) To defect once and then cooperate thereafter (being punished once) To defect and continue defecting thereafter

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Defect once Gain: 70 Loss: 150 in the next period Worthy if 70>150/(1+r) or r>114%

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Defect forever Gain: 70 Loss: 50 for the rest of periods Worthy if 70>50/(1+r)+50/(1+r)^2+… or 70>50/r or r>71.4% To cooperate is the N.E. in infinitely repeated game for relative low r

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What if Shagri-La playing grim strategy is common knowledge? Implication?

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