國(guó)外博弈論課件lecture(1)-資料下載頁(yè)
2024-10-19 13:57本頁(yè)面
【正文】 1)+(1–r) 1 = 1 – 2r ? EU2(H, (r, 1–r)) = EU2(T, (r, 1–r)) 2r – 1= 1 – 2r 4r = 2 This give us r = 1/2 ? Hence, ((, ), (, )) is a mixed strategy Nash equilibrium by Theorem 2. Matching pennies Player 2 H ( q ) T ( 1–q ) Player 1 H ( r ) 1 , 1 1 , 1 T ( 1–r ) 1 , 1 1 , 1 May 29, 2021 73347 Game TheoryLecture 8 22 ? Employee’s expected payoff of playing “work” ? EU1(Work, (q, 1–q)) = q 50 + (1–q) 50=50 ? Employee’s expected payoff of playing “shirk” ? EU1(Shirk, (q, 1–q)) = q 0 + (1–q) 100=100(1–q) ? Employee is indifferent between playing Work and Shirk. ? 50=100(1–q) ? q=1/2 Use Theorem 2 to find mixed strategy Nash equilibrium: illustration Employee Monitoring Manager Monitor ( q ) Not Monitor (1–q ) Employee Work (r) 50 , 90 50 , 100 Shirk (1–r) 0 , 10 100 , 100 May 29, 2021 73347 Game TheoryLecture 8 23 ? Manager’s expected payoff of playing “Monitor” ? EU2(Monitor, (r, 1–r)) = r 90+(1–r) (10) =100r–10 ? Manager’s expected payoff of playing “Not” ? EU2(Not, (r, 1–r)) = r 100+(1–r) (100) =200r–100 ? Manager is indifferent between playing Monitor and Not 100r–10 =200r–100 implies that r=. ? Hence, ((, ), (, )) is a mixed strategy Nash equilibrium by Theorem 2. Use Theorem 2 to find mixed strategy Nash equilibrium: illustration Employee Monitoring Manager Monitor ( q ) Not Monitor (1–q ) Employee Work (r) 50 , 90 50 , 100 Shirk (1–r) 0 , 10 100 , 100 May 29, 2021 73347 Game TheoryLecture 8 24 ? Use Theorem 2 to find a mixed Nash equilibrium Use Theorem 2 to find mixed strategy Nash equilibrium: illustration Battle of sexes Pat Opera (q) Prize Fight (1q) Chris Opera ( r ) 2 , 1 0 , 0 Prize Fight (1r) 0 , 0 1 , 2 May 29, 2021 73347 Game TheoryLecture 8 25 ? Use Theorem 2 to find a mixed Nash equilibrium Use Theorem 2 to find mixed strategy Nash equilibrium: illustration Example Player 2 L (q) R (1q) Player 1 T ( r ) 6 , 4 2 , 6 B (1r) 3 , 3 6 , 1 May 29, 2021 73347 Game TheoryLecture 8 26 Summary ? Mixed strategies ? Mixed Nash equilibrium ? Find mixed Nash equilibrium ? Next time ? 2player game each with a finite number of strategies ? Reading lists ? Chapter of Gibbons and Cha of Osborne
教學(xué)課件相關(guān)推薦
鄂ICP備17016276號(hào)-1