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Part 2-3 Repeated Game

Part 2-3 Repeated Game. prolog. Intuition ： the role of repeated play Folk theorem( 無名氏定理 ) ： The wildly held intuition that noncooperative games played repeatedly may often have cooperative equilibria . One-off game ： noncooperative solution cooperative solution

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Part 2-3 Repeated Game

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  1. Part 2-3 Repeated Game

  2. prolog • Intuition：the role of repeated play • Folk theorem(無名氏定理)： The wildly held intuition that noncooperative games played repeatedly may often have cooperative equilibria.

  3. One-off game：noncooperative solution cooperative solution using sequential game to test the intuition intuition can be very misleading when repeated play has an end point.

  4. Camper’s Dilemma(simultaneous game) NE：（don’t, don’t）exhibits social dilemma.

  5. two stage game：the same simultaneous game plays twice

  6. two stage game： Four basic proper subgame. Applying backward induction, the SPNE is（don’t, don’t） • N-round We extend this reasoning to N stages. As long as the N is limited number of time, the best-response strategy in last round is always the noncooperative “ don’t” strategy as in first round. That says no cooperative strategy will ever played.

  7. 玩有限次的重複賽局：當一次賽局有一純策略納許均衡時，則此納許均衡被重複玩就是重複賽局的子賽局完美均衡。玩有限次的重複賽局：當一次賽局有一純策略納許均衡時，則此納許均衡被重複玩就是重複賽局的子賽局完美均衡。

  8. Pressing game（sequential game） SPNE：（N, （PN, NN）） Outcome：A takes “N”

  9. two-round repeated game

  10. two-round repeated game If A persuade the B to take “ care” by threatening to retaliate. A might, for example, response to a “no care” strategy by taking “ no pressing” the following round. Suppose A takes a Tit- for-Tat strategy rule： 「The player’s strategy in this round depends on the opponent’s choice in last round」

  11. Is the Tit-for-Tat strategy a credible threat and promise？ Credibility is associated with SPNE Note：本期合作之目的乃在營造次期合作 的氣氛，若無次期，本期即無合作 之必要。

  12. Is the threat credible？：light gray oval If B1 takes “no care”, then A2 takes “ no pressing” • Since -1>-2, the threat is credible.

  13. Is the promise credible？：dark gray oval If B1 takes “ care”, then A2 takes “pressing” The “no pressing” is A2’s best response because he anticipates that B2 will take “no care” in this round. The “no care” is B2’s best response since there is no next round. So, the promise is incredible.

  14. player A cannot play a Tit-for-Tat rule on 2nd round, last round. SPNE：as in one round • Extension：T round, limited number of times Tndround：不合作T-1nd round：不合作 …1stround：不合作

  15. Folk theorem is not applicable to noncooperative games that repeated a definite number of times. 非合作均衡策略重複T次乃是此重複賽局唯一的SPNE

  16. the Chain store Paradox Since retaliation is not subgame perfect onthe last play, any threat to retaliation will not be credible.

  17. The payoff depends on the motivation 恐嚇取財的 挾持賽局 以殺人為目的 的挾持賽局

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