# Repeated Games and the Prisoner’s Dilemma. Prisoner’s dilemma What if the game is played “repeatedly” for several periods? DefectCooperate Defect10 yr,

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Repeated Games and the Prisoner’s Dilemma

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

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, 200320, 100 Peaceful100, 320250, 250

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.

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

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

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

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

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

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