More Related Content Similar to 逐次均衡【精緻化】 (14) More from ssusere0a682 (20) 逐次均衡【精緻化】5. ҎԼͷల։ܗήʔϜͰද͞ݱΕΔήʔϜΛσʔτήʔϜͱ͢ʹͱ͜ͿݺΔ
σʔτήʔϜʹ͓͚Δ෦ήʔϜશߧۉΛٻΊΑ
෦ήʔϜʹ͓͚ΔφογϡߧۉΛߟ͑Δͱ
ͱ Ͱ͋Δ
ɾ෦ήʔϜͰ ͕औΒΕΔͱ͢ΕϓϨΠϠʔ ΛબͿͷ͕࠷ద
ɾ෦ήʔϜͰ ͕औΒΕΔͱ͢Ε
ϓϨΠϠʔ ΛબͿͷ͕࠷ద
Ώ͑ʹ
෦ήʔϜશߧۉ
(movie, movie) (shopping, shopping)
(movie, movie) home
(shopping, shopping)
out
(home − movie, movie) (out − shopping, shopping)
σʔτήʔϜʹ͓͚Δ෦ήʔϜશߧۉ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
1ʘ2
movie
shopping
movie shopping
෦ήʔϜ
෦ήʔϜ
P1
(2, 0)
home out
(1, 3)
P1
(2, 0)
home out
(3, 1)
6. ҎԼͷల։ܗήʔϜͰද͞ݱΕΔήʔϜΛσʔτήʔϜͱ͢ʹͱ͜ͿݺΔ
σʔτήʔϜʹ͓͚ΔશϕΠδΞϯߧۉΛٻΊΑ
શϕΠδΞϯߧۉ
ͨͩ͠
ͨͩ͠
φογϡͱߧۉಉ͡ઓུͷΛؚΈ
෦ήʔϜશͰߧۉഉআͰ͖ͨઓུͷؚΜͰ͠·͍ͬͯΔ
ஞ࣍ߧۉΛͬͯΈͯʁ
(home − movie, movie) μ1
1 μ1
2 μ2
(1,1,(r,1 − r)) r ≥
1
4
(home − shopping, movie) μ1
1 μ1
2 μ2
(1,1,(r,1 − r)) r ≥
1
4
(out − shopping, shopping) μ1
1 μ1
2 μ2
(1,1,(0,1))
σʔτήʔϜʹ͓͚ΔऑશϕΠδΞϯߧۉ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
μ1
1 = 1
μ1
2 = 1
r 1 − r
7. ऑ
શϕΠδΞϯߧۉ
શϕΠδΞϯߧۉઓུͷ ͱ৴೦ͷମܥ ͷ Ͱ
͕ ͷͱͰஞ࣍߹ཧతͰ͋Γ
͕ ʹ߹తͰ͋ΔͷΛऑશϕΠδΞϯ͏͍ͱߧۉ
ߦಈઓུͷஞ࣍߹ཧੑల։ܗήʔϜ ʹ͓͍ͯ
৴೦ͷମܥ ͕༩͑ΒΕ͍ͯΔͱ͢Δ
͜ͷͱ͖
ઓུͷ ͕
ϓϨΠϠʔ ͷใू߹ ʹ͓͍ͯҎԼΛຬͨ͢ͱ͖
৴೦ͷମܥ ͷͱͰใू߹ ʹ͓͍ͯஞ࣍߹ཧతͰ͋Δͱ͍͏
৴೦ͷମͱܥ߹ੑల։ܗήʔϜ ʹ͓͍ͯ
ઓུͷ ͕༩͑ΒΕ͍ͯΔͱ͢Δ
͜ͷͱ͖
৴೦ͷମܥ ͕
ҙͷϓϨΠϠʔ ͷҙͷใू߹ ʹ͓͍ͯ
Ͱ͋Ε
ͯ͢ͷ ͷ ʹ͍ͭͯ
ͱͳΔͱ͖
ઓུͷ ʹ͓͍ͯ߹తͰ͋Δͱ͍͏
b μ (b, μ)
b μ μ b
Γ μ
b = (b1
, ⋯, bn
) i ui
l
b μ ui
l
Hi
(ui
l, μ, (bi,ui
l, b−i,ui
l)) ≥ Hi
(ui
l, μ, (b′

i,ui
l, b−i,ui
l)), ∀b′

i,ui
l ∈ Bi,ui
l
Γ b = (b1
, ⋯, bn
)
μ i ui
l
Prob(ui
l |b) 0 ui
l x*
μ(x*) =
Prob(x*|b)
∑x∈ui
l
Prob(x|b)
μ b
ߦಈઓུʹΑͬͯ౸ୡՄೳͳ
ܦ࿏ʹ͓͚Δ߹ཧੑͷΈߟ͑Δ
8. ߦಈઓུͷ͕શʹ֬త
ߦಈઓུͷ ͕શʹ֬తͰ͋Δͱ
ͯ͢ͷࢬʹ͍ͭͯਖ਼ͷ֬Λ༩͑Δͱ͖Λ͍͏
b = (b1
, ⋯, bn
)
ߦಈઓུͷ͕શʹ֬త
P1
P2
P1
(2, 0)
(0, 0)
home
ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
μ1
1 = 1
μ1
2 = 1
r 1 − r
P1
P2
P1
(2, 0)
(0, 0)
home
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
μ1
1 = 1
μ1
2 = 1
r 1 − r
શʹ֬తͳߦಈઓུ
Ͱ͋ΕͲͷใू߹
ඞͣ౸ୡ͢Δ
શʹ֬తͰͳ͍ શʹ֬తͰ͋Δ
9. ஞ࣍ߧۉ
ஞ࣍ߧۉઓུͷ ͱ৴೦ͷମܥ ͷ ͕ஞ࣍͋ͰߧۉΔͱ
શʹ֬తͳߦಈઓུͷͱ৴೦ͷ
ମܥͷྻ ͕ଘࡏͯ͠
ҎԼΛຬͨ͢ɿ
ߦಈઓུͷஞ࣍߹ཧੑ৴೦ͷମܥ ʹରͯ͠
ઓུͷ ͕
ϓϨΠϠʔ ͷใू߹ ʹ͓͍ͯ
৴೦ͷମͱܥ߹ੑ֤ ʹ͍ͭͯ
৴೦ͷମܥ ߦಈઓུͷ ͔Βಋ͔Ε
͕Γཱͭ
͜͜Ͱ
ߦಈઓུͷ ͔Βಋ͔ΕΔͱ
ϕΠζͷϧʔϧΛ༻͍ͯ
ͱͳΔͱ͖Λ͍͏
b μ (b, μ)
{(bk, μk)}∞
k=1
μ b = (b1
, ⋯, bn
) i ui
l
Hi
(ui
l, μ, (bi,ui
l, b−i,ui
l)) ≥ Hi
(ui
l, μ, (b′

i,ui
l, b−i,ui
l)), ∀b′

i,ui
l ∈ Bi,ui
l
k = 1, 2, ⋯ μk bk = (b1
k , ⋯, bn
k )
(bk, μk) → (b, μ) k → ∞
bk = (b1
k , ⋯, bn
k )
μk(x*) =
Prob(x*|bk)
∑x∈ui
l
Prob(x|bk)
x* x**
μk(x*) =
1
3
1
3
+ 1
4
=
4
7
ui
l
1
3
y
1
4
5
12
ऑશϕΠδΞϯͱߧۉಉ͡
શʹ֬తͳߦಈઓུʹΑͬͯ
ͯ͢ͷܦ࿏ʹ͓͚Δ߹ཧੑΛߟ͑Δ
10. σʔτήʔϜʹ͓͚Δஞ࣍ߧۉΛ֬ೝ͢Δ
શϕΠδΞϯݕ͍ͯͭʹߧۉ౼
ͨͩ͠
ϓϨΠϠʔͷߦಈઓུ
ϓϨΠϠʔͷߦಈઓུ
ͨͩ͠
ͱ͢Δ͢Δͱ
͜ͷͱ͖
͜ͷߦಈઓུ͔Βಋ͔ΕΔ৴೦ ࣗ໌ͳͷআ͘
͜ʹٯͷ৴೦ͷମ ܥ
ͷͰݩ
ϓϨΠϠʔͷߦಈઓུ ࠷ద
͜ͷߦಈઓུʹରͯ͠ϓϨΠϠʔͷߦಈઓུ ࠷ద
Ώ͑ʹ
ஞ࣍ ߧۉ
(home − movie, movie) μ1
1 μ1
2 μ2
(1,1,(r,1 − r)) r ≥
1
4
b1
k = ((1 − ϵ1
k , ϵ1
k ), (1 − ϵ′

1
k , ϵ′

1
k )) b2
k = ((1 − ϵ2
k , ϵ2
k ))
ϵ1
k → 0 ϵ′

1
k → 0 ϵ2
k → 0 k → ∞
b1
k = ((1 − ϵ1
k , ϵ1
k ), (1 − ϵ′

1
k , ϵ′

1
k )) → ((1,0), (1,0)) b2
k = ((1 − ϵ2
k , ϵ2
k )) → ((1,0))
r =
ϵ1
k (1 − ϵ′

1
k )
ϵ1
k (1 − ϵ′

1
k ) + ϵ1
k ϵ′

1
k
→ 1 (k → ∞)
μ1
1 μ1
2 μ2
(1,1,(1,0))
b2
= ((1,0))
((1,0), (1,0))
(home − movie, movie) μ1
1 μ1
2 μ2
(1,1,(1,0))
σʔτήʔϜͰ֬ೝ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
μ1
1 = 1
μ1
2 = 1
r 1 − r
ϵ1
k
ϵ′

1
k
ϵ2
k
ϵ2
k
ߦಈઓུͰهड़͢Ε
b = (b1
, b2
) = (((1,0), (1,0)), ((1,0)))
1 0
11. σʔτήʔϜʹ͓͚Δஞ࣍ߧۉΛ֬ೝ͢Δ
શϕΠδΞϯݕ͍ͯͭʹߧۉ౼
ͨͩ͠
ϓϨΠϠʔͷߦಈઓུ
ϓϨΠϠʔͷߦಈઓུ
ͨͩ͠
ͱ͢Δ͢Δͱ
͜ͷͱ͖
͜ͷߦಈઓུ͔Βಋ͔ΕΔ৴೦ ࣗ໌ͳͷআ͘
͜ʹٯͷ৴೦ͷମ ܥ
ͷͰݩ
ϓϨΠϠʔͷߦಈઓུ ࠷దͰͳ͍
Ώ͑ʹ
ߦಈઓུͷ ஞ࣍Ͱߧۉͳ͍
(home − shopping, movie) μ1
1 μ1
2 μ2
(1,1,(r,1 − r)) r ≥
1
4
b1
k = ((1 − ϵ1
k , ϵ1
k ), (ϵ′

1
k ,1 − ϵ′

1
k )) b2
k = ((1 − ϵ2
k , ϵ2
k ))
ϵ1
k → 0 ϵ′

1
k → 0 ϵ2
k → 0 k → ∞
b1
k = ((1 − ϵ1
k , ϵ1
k ), (ϵ′

1
k ,1 − ϵ′

1
k )) → ((1,0), (0,1)) b2
k = ((1 − ϵ2
k , ϵ2
k )) → ((1,0))
r =
ϵ1
k ϵ′

1
k
ϵ1
k ϵ′

1
k + ϵ1
k (1 − ϵ′

1
k )
→ 0 (k → ∞)
μ1
1 μ1
2 μ2
(1,1,(0,1))
b2
= ((1,0))
(home − movie, movie)
σʔτήʔϜͰ֬ೝ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
μ1
1 = 1
μ1
2 = 1
r 1 − r
ϵ1
k
ϵ′

1
k
ϵ2
k
ϵ2
k
ߦಈઓུͰهड़͢Ε
b = (b1
, b2
) = (((1,0), (0,1)), ((1,0)))
0 1
12. σʔτήʔϜʹ͓͚Δஞ࣍ߧۉΛ֬ೝ͢Δ
શϕΠδΞϯݕ͍ͯͭʹߧۉ౼
ϓϨΠϠʔͷߦಈઓུ
ϓϨΠϠʔͷߦಈઓུ
ͨͩ͠
ͱ͢Δ͢Δͱ
͜ͷͱ͖
͜ͷߦಈઓུ͔Βಋ͔ΕΔ৴೦ ࣗ໌ͳͷআ͘
͜ʹٯͷ৴೦ͷମ ܥ
ͷͰݩ
ϓϨΠϠʔͷߦಈઓུ ࠷దͰ͋Δ
͜ͷߦಈઓུʹରͯ͠ϓϨΠϠʔͷߦಈઓུ ࠷ద
Ώ͑ʹ
ஞ࣍ ߧۉ
(out − shopping, shopping) μ1
1 μ1
2 μ2
(1,1,(0,1))
b1
k = ((ϵ1
k ,1 − ϵ1
k ), (ϵ′

1
k ,1 − ϵ′

1
k )) b2
k = ((ϵ2
k ,1 − ϵ2
k ))
ϵ1
k → 0 ϵ′

1
k → 0 ϵ2
k → 0 k → ∞
b1
k = ((ϵ1
k ,1 − ϵ1
k ), (ϵ′

1
k ,1 − ϵ′

1
k )) → ((0,1), (0,1)) b2
k = ((ϵ2
k ,1 − ϵ2
k )) → ((0,1))
r =
(1 − ϵ1
k )ϵ′

1
k
(1 − ϵ1
k )ϵ′

1
k + (1 − ϵ1
k )(1 − ϵ′

1
k )
→ 0 (k → ∞)
μ1
1 μ1
2 μ2
(1,1,(0,1))
b2
= ((0,1))
((0,1), (0,1))
(out − shopping, shopping) μ1
1 μ1
2 μ2
(1,1,(0,1))
σʔτήʔϜͰ֬ೝ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
μ1
1 = 1
μ1
2 = 1
r 1 − r
ϵ1
k
ϵ′

1
k
ϵ2
k
ϵ2
k
ߦಈઓུͰهड़͢Ε
b = (b1
, b2
) = (((0,1), (0,1)), ((0,1)))
0 1