Repeated Games and the Prisoners Dilemma Defect Cooperate

Repeated Games and the Prisoner’s Dilemma

¢ ¢ Defect Cooperate Defect 10 yr, 10 yr 1 yr, 25 yr Cooperate 25 yr, 1 yr 3 yr, 3 yr Prisoner’s dilemma What if the game is played “repeatedly” for several periods?

¢ ¢ ¢ Aggressive Peaceful Aggressive 200, 200 320, 100 Peaceful 100, 320 250, 250 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?

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 l Tit-for-tat (TFT) l

¢ 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) l To defect and continue defecting thereafter l

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

¢ Defect forever Gain: 70 l Loss: 50 for the rest of periods l 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? ¢