國外博弈論課件lecture(11)-資料下載頁
2024-10-18 12:47本頁面
【正文】 trig ger strat egy if 41??. 1 2 t1 t t+1 t+2 Stage (R1, R2) (R1, R2) (R1, R2) (R1, R2) (R1, R2) (R1, R2) (R1, R2) (R1, R2) (R1, R2) (R1, L2) (L1, L2) (L1, L2) P2: Trigger P2: deviate trigger at t June 18, 2021 73347 Game TheoryLecture 21 16 Trigger strategy: step 2 ? Step 2: check whether the Nash equilibrium induces a Nash equilibrium in every subgame of the infinitely repeated game. ? Recall that every subgame of the infinitely repeated game is identical to the infinitely repeated game as a whole June 18, 2021 73347 Game TheoryLecture 21 17 Step 2 cont’d: subgame 1 L1 R1 2 L2 R2 2 L2 R2 L1 R1 2 L2 R2 2 L2 R2 L1 R1 2 L2 R2 2 L2 R2 L1 R1 2 L2 R2 2 L2 R2 L1 R1 2 L2 R2 2 L2 R2 1 1 5 0 0 5 4 4 1 1 1 1 (1, 1) (5, 0) (0, 5) (4, 4) 1 1 5 0 0 5 4 4 1 1 5 0 0 5 4 4 1 1 5 0 0 5 4 4 TO INFINITY June 18, 2021 73347 Game TheoryLecture 21 18 Trigger strategy: step 2 cont’d ? We have two classes of subgames: ? subgame following a history (from stage 1) in which the stage outes are all (R1, R2) ? subgame following a history (from stage 1) in which at least one stage oute is not (R1, R2) ? The Nash equilibrium of the infinitely repeated game induces a Nash equilibrium in which each player still plays trigger strategy for the first class of subgames ? The Nash equilibrium of the infinitely repeated game induces a Nash equilibrium in which (L1, L2) is played forever for the second class of subgames. June 18, 2021 73347 Game TheoryLecture 21 19 Summary ? Finitely repeated games ? Infinitely repeated games ? Next time ? Infinitely repeated games ? Static games of inplete information ? Reading lists ? Sec AC of Gibbons ? Sec of Gibbons
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