國外博弈論課件lecture(12)-資料下載頁
2024-10-18 12:47本頁面
【正文】 a se quenc e of payoffs 5 , 1 , 1 , 1 ... (fr o m sta ge t t o st age + ∞ ). D isc ounti n g the se payoff s to st ag e t g ive s us ????????????15. . . . . .111532 June 17, 2021 73347 Game TheoryLecture 20 24 Trigger strategy: step 1 cont’d Stage 1: (R1, R2) Stage 2: (R1, R2) Stage t1: (R1, R2) Stage t: (R1, L2) Stage t+1: (L1, L2) Stage t+2: (L1, L2) 41 1514?????????? ? Hence, if 41??, pla yer 2 c ann ot be better of f if she devi ates f rom the tr igge r strate gy. ? This i m pli es t hat i f pl ayer 1 plays the tri gge r str a te gy the pla yer 239。 s best re spon se is the tr igger strate gy f or 41??. ? By sy mm et ry, i f player 2 pla ys the tri gger str a te gy the n pla yer 139。 s bes t r e sponse is t he tr igger strate gy. ? Hence, the re is a Nash e q uil ib ri um in whic h both pl ayers pla y the trig ger strat egy if 41??. June 17, 2021 73347 Game TheoryLecture 20 25 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 Stage 1: (R1, R2) Stage 2: (R1, R2) Stage t1: (R1, R2) Stage t: (R1, R2) Stage t+1: (R1, R2) Stage t+2: (R1, R2) June 17, 2021 73347 Game TheoryLecture 20 26 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 17, 2021 73347 Game TheoryLecture 20 27 Trigger strategy: step 2 cont’d ? We have two classes of subgames: ? subgame following a history in which the stage outes are all (R1, R2) ? subgame following a history 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 17, 2021 73347 Game TheoryLecture 20 28 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
教學(xué)課件相關(guān)推薦
鄂ICP備17016276號(hào)-1