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Repeated Games and the Prisoner’s Dilemma

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

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Repeated Games and the Prisoner’s Dilemma

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  1. Repeated Games and the Prisoner’s Dilemma

  2. Prisoner’s dilemma • What if the game is played “repeatedly” for several periods?

  3. 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?

  4. 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.

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

  6. 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

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

  8. 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

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

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