國外博弈論課件lecture(19)(編輯修改稿)
2024-11-14 12:47 本頁面
【文章內(nèi)容簡介】 e 3: check whether there is a mixed strategy in which p110, p120, p210, p22=0, p230 ? By theorem 4, we should have 2?p11+2? p12 = 3?p11+2? p12 ? 3?p11+1? p12 and p11+p12=1. ? Consider 2?p11+2? p12= 3?p11+2? p12 2?p11= 3?p11 Hence, p11= 0. This contradicts the condition p110. Hence, there is no Nash equilibrium in this case. Player 2 L (p21) M (p22) R (p23) Player 1 T (p11) 2 , 2 0 , 3 1 , 3 B (p12) 3 , 2 1 , 1 0 , 2 June 6, 2021 73347 Game TheoryLecture 14 13 Exercise of Osborne ? Case 4: check whether there is a mixed strategy in which p110, p120, p21=0, p220, p230 ? By theorem 4, we should have 2?p11+2? p12? 3?p11+1? p12 = 3?p11+2? p12 and p11+p12=1. ? Consider 3?p11+1? p12 = 3?p11+2? p12 1?p12= 2?p12 Hence, p12= 0. This contradicts the condition p120. Hence, there is no Nash equilibrium in this case. Player 2 L (p21) M (p22) R (p23) Player 1 T (p11) 2 , 2 0 , 3 1 , 3 B (p12) 3 , 2 1 , 1 0 , 2 June 6, 2021 73347 Game TheoryLecture 14 14 Exercise of Osborne ? Case 5: check whether there is a mixed strategy in which p110, p120, p210, p22=0, p23=0 (Note this implies p21=1) ? By theorem 4, we should have 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 and p21+ p22+ p23 = 1 ? Plugging p21=1, p22=0, p23=0 into 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 gives us 2=3, which is a contradiction. Hence, there is no Nash equilibrium in this case. Player 2 L (p21) M (p22) R (p23) Player 1 T (p11) 2 , 2 0 , 3 1 , 3 B (p12) 3 , 2 1 , 1 0 , 2 June 6, 2021 73347 Game TheoryLecture 14 15 Exercise of Osborne ? Case 6: check whether there is a mixed strategy in which p110, p120, p21=0, p220, p23=0 (Note this implies p22=1) ? By theorem 4, we should have 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 and p21+ p22+ p23 = 1 ? Plugging p21=0, p22=1, p23=0 into 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 gives us 0=1, which is a contradiction. Hence, there is no Nash equilibrium in this case. Player 2 L (p21) M (p22) R (p23) Player 1 T (p11) 2 , 2 0 , 3 1 , 3 B (p12) 3 , 2 1 , 1 0 , 2 June 6, 2021 73347 Game TheoryLecture 14 16 Exercise of Osborne ? Case 7: check whether there is a mixed strategy in which p110, p120, p21=0, p22=0, p230 (Note this implies p23=1) ? By theorem 4, we should have 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 and p21+ p22+ p23 = 1 ? Plugging p21=0, p22=0, p23=1 into 2?p21+0? p22+1? p23 =3?p21+1? p22+0? p23 gives us 1=0, which is a contradiction. Hence, there is no Nash equilibrium in this case. Player 2 L (p21) M (p22) R (p23) Player 1 T (p11) 2 , 2 0 , 3 1 , 3 B (p12) 3 ,
教學課件相關推薦
鄂ICP備17016276號-1