https://www.nicovideo.jp/watch/sm38456327 https://youtu.be/NGa3Kgaql9c

1. ήʔϜཧ࿦#4*$ୈճ
ల։‫ܗ‬ήʔϜʹ͓͚Δઓུɾ‫ظ‬଴རಘ

2. 1. ల։‫ܗ‬ήʔϜʹ͓͚ΔઓུΛཧղ
2. ల։‫ܗ‬ήʔϜʹ͓͚Δ‫ظ‬଴རಘΛཧղ
ຊಈըͷ໨త

3. 1. ల։‫ܗ‬ήʔϜʹ͓͚Δઓུ
(1)ల։‫ܗ‬ήʔϜͷఆٛ (෮श)
(2)७ઓུ
(3)ࠞ߹ઓུ
(4)‫ॴہ‬ઓུͱߦಈઓུ
(5)ઓུ·ͱΊ
2. ల։‫ܗ‬ήʔϜʹ͓͚Δ‫ظ‬଴རಘ
(1)७ઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
(2)ࠞ߹ઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
(3)ߦಈઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
(4)ඪ४Խ
໨࣍

4. Strategies in Extensive form game
ల։‫ܗ‬ήʔϜʹ͓͚Δઓུ

5. ల։‫ܗ‬ήʔϜͷఆٛ
ల։‫ܗ‬ήʔϜ
ϓϨΠϠʔͷू߹Λ ͱ͢Δ
Λల։‫ܗ‬ήʔϜͱ‫Ϳݺ‬
༗޲໦
ϓϨΠϠʔ෼ׂ
‫ۮ‬વख൪ͷ֬཰෼෍଒
৘ใ෼ׂ
རಘؔ਺
N = {1,2,3,⋯, n}
Γ = (K, P, p, U, h)
K = (V, E)
P = [P0
, P1
, ⋯, Pn
]
p
U = [U0
, U1
, ⋯, Un
]
h
u1
1
u2
1
u2
2
u0
1
N
P1
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2

6. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ͭ·Γ
ϓϨΠϠʔͷ७ઓུΛ ͱ͢Δͱ
ΛϓϨΠϠʔͷ৘ใू߹ͷ਺ͱͯ͠
Ͱ͋Δ
ϓϨΠϠʔͷ७ઓུͷू߹Λ Ͱද͢
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
i si
k(i) i
si
: Ui
→
k(i)
⋃
l=1
A(ui
l)
si
(ui
l) = ai
∈ A(ui
l), ∀ui
l ∈ Ui
i Si
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

7. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

8. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

9. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

10. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

11. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

12. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

13. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

14. ७ઓུ
७ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶ ΛׂΓ౰ͯΔؔ਺Λ७ઓུͱ͍͏
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
ai
∈ A(ui
l)
s1
1(u1
1) = a1
1
s1
2(u1
1) = a1
2
s2
1(u2
1) = a2
1 s2
1(u2
2) = a2
3
s2
2(u2
1) = a2
2 s2
2(u2
2) = a2
3
s2
3(u2
1) = a2
1 s2
3(u2
2) = a2
4
s2
4(u2
1) = a2
2 s2
4(u2
2) = a2
4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
ઓུ
ઓུ
a1
1
a1
2
ઓུ
ઓུ
ઓུ
ઓུ
a2
1 − a2
3
a2
2 − a2
3
a2
1 − a2
4
a2
2 − a2
4

15. ࠞ߹ઓུ
ࠞ߹ઓུ
ϓϨΠϠʔ ʹରͯ͠७ઓུͷू߹ ্ͷ֬཰෼෍
Λࠞ߹ઓུͱ͍͏ࠞ߹ઓུͷू߹Λ ͱ͢Δ
ϓϨΠϠʔʹ͍ͭͯࠞ߹ઓུ
ϓϨΠϠʔʹ͍ͭͯࠞ߹ઓུ
i ∈ N Si
qi
= (qi
(si
))si∈Si Qi
q1
q1
(s1
1(u1
1)) q1
(a1
1)
q1
(s1
2(u1
1)) q1
(a1
2)
q2
q2
(s2
1) = q2
(a2
1 − a2
3)
q2
(s2
2) = q2
(a2
2 − a2
3)
q2
(s2
3) = q2
(a2
1 − a2
4)
q2
(s2
4) = q2
(a2
2 − a2
4)
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1

16. ‫ॴہ‬ઓུͱߦಈઓུ
‫ॴہ‬ઓུ
ϓϨΠϠʔ ʹର֤ͯ͠৘ใू߹ ʹ͓͚Δ
બ୒ࢶͷू߹ ্ͷ֬཰෼෍ Λ‫ॴہ‬ઓུͱ͍͏
ߦಈઓུ
ϓϨΠϠʔ ʹରͯ͠ Λ
ߦಈઓུͱ͍͏ߦಈઓུͷू߹Λ ͱ͢Δ
ϓϨΠϠʔʹ͍ͭͯ
ϓϨΠϠʔʹ͍ͭͯ
i ∈ N ui
l ∈ Ui
A(ui
l) bi
ui
l
i ∈ N bi
= {bi
ui
l
}ui
l∈Ui
Bi
b1
= ((b1
u1
1
(a1
1), b1
u1
1
(a1
2)))
b2
= ((b2
u2
1
(a2
1), b2
u2
1
(a2
2)) ((b2
u2
2
(a2
3) b2
u2
2
(a2
4)))
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
‫ॴہ‬ઓུɿ
(b1
u1
1
(a1
1), b1
u1
1
(a1
2))
‫ॴہ‬ઓུɿ
(b2
u2
1
(a2
1), b2
u2
1
(a2
2))
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b2
u2
1
(a2
1)
b2
u2
1
(a2
2)
b2
u2
2
(a2
3)
b2
u2
2
(a2
4)

17. ઓུ·ͱΊ
ϓϨΠϠʔͷઓུʹߦಈ‫ܭ‬ը
७ઓུɾࠞ߹ઓུɾߦಈઓུ
ల։‫ܗ‬ήʔϜʹ͓͍ͯ
֤৘ใू߹ͰͷߦಈΛߟ͑Δͱ͍͏఺͔Β
ࠞ߹ઓུΑΓߦಈઓུͷํ͕ద੾
˒‫׬‬શ‫ه‬ԱήʔϜͰ͸
ࠞ߹ઓུͱߦಈઓུͰୡ੒Ͱ͖Δ
‫ظ‬଴རಘ͸Ұக͢Δ
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b2
u2
1
(a2
1)
b2
u2
1
(a2
2)
b2
u2
2
(a2
3)
b2
u2
2
(a2
4)

18. Expected Payoff in Extensive form game
ల։‫ܗ‬ήʔϜʹ͓͚Δ‫ظ‬଴རಘ

19. ७ઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
࢝఺͔Βऴ఺ ΁ͷύε্ʹ͓͚Δ
શͯͷબ୒ࢶͷશମΛ ͱ͢Δ ྫ
͸
‫ۮ‬વख൪ͷબ୒ࢶͷू߹ ྫ
֤ϓϨΠϠʔͷબ୒ࢶͷू߹ ྫ
͔ΒͳΔ
Λू߹ ʹ‫·ؚ‬ΕΔ‫ۮ‬વख൪ͷ͢΂ͯͷબ୒ࢶ͕
બ୒͞ΕΔ֬཰ͷੵͱ͢Δ
͢ͳΘͪ
·ͨ
΁ͷύεʹ‫ۮ‬વख൪Λ‫͍ͳ·ؚ‬৔߹͸
ྫ
w ∈ W
E(w) E(w4) = {a0
1, a1
2, a2
2}
E(w)
E0
(w) E0
(w4) = {a0
1}
i Ei
(w) E1
(w4) = {a1
2} E2
(w4) = {a2
2}
c(w) E0
(w) e
c(w) =
∏
e∈E0
(w)
p(e)
w ∈ W c(w) = 1
c(w4) =
1
2
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
p01
(a0
1) =
1
2
p01
(a0
2) =
1
2
w4

20. ७ઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
७ઓུͷ૊ ʹରͯ͠
࢝఺͔Βऴ఺ ΁ͷ౸ୡ͢Δ֬཰Λ ͱ͢Δ
֤ ͕ ͷ͢΂ͯͷબ୒ࢶΛબͿͷͰ͋Ε͹
ͦ͏Ͱͳ͚Ε͹
ϓϨΠϠʔ ͷ‫ظ‬଴རಘ͸
ྫ
ϓϨΠϠʔͷ७ઓུΛ
ϓϨΠϠʔͷ७ઓུΛ ͱ͢Δ
s = (s1
, ⋯, sn
)
w ∈ W p(w|s)
si
Ei
(w) p(w|s) = c(w)
p(w|s) = 0
i ∈ N
Hi
(s) =
∑
w∈W
p(w|s)hi
(w)
a1
2 a2
2 − a2
3
E1
(w4) = {a1
2} E2
(w4) = {a2
2} p(w4 |s) = c(w4) = 1/2
E1
(w7) = {a1
2} E2
(w7) = {a2
3} p(w7 |s) = c(w7) = 1/2
H1
(s) = p(w4 |s)h1
(w4) + p(w7 |s)h1
(w7) =
1
2
⋅ 6 +
1
2
⋅ 2 = 4
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
p01
(a0
1) =
1
2
p01
(a0
2) =
1
2
w4
w7

21. ७ઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
७ઓུͷ૊ ʹରͯ͠
࢝఺͔Βऴ఺ ΁ͷ౸ୡ͢Δ֬཰Λ ͱ͢Δ
֤ ͕ ͷ͢΂ͯͷબ୒ࢶΛબͿͷͰ͋Ε͹
ͦ͏Ͱͳ͚Ε͹
ϓϨΠϠʔ ͷ‫ظ‬଴རಘ͸
s = (s1
, ⋯, sn
)
w ∈ W p(w|s)
si
Ei
(w) p(w|s) = c(w)
p(w|s) = 0
i ∈ N
Hi
(s) =
∑
w∈W
p(w|s)hi
(w)
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
p01
(a0
1) =
1
2
p01
(a0
2) =
1
2
̍c
a1
1
a1
2
a2
1 − a2
3
a2
2 − a2
3
a2
1 − a2
4
a2
2 − a2
4

22. ࠞ߹ઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
ࠞ߹ઓུͷ૊ ʹରͯ͠
࢝఺͔Βऴ఺ ΁ͷ౸ୡ͢Δ֬཰Λ ͱ͢Δ
ϓϨΠϠʔ ͷ‫ظ‬଴རಘ͸
ྫ
ϓϨΠϠʔͷࠞ߹ઓུΛ
ϓϨΠϠʔͷࠞ߹ઓུΛ ͱ͢Δ
q = (q1
, ⋯, qn
)
w ∈ W p(w|q)
p(w|q) =
∑
s1
∈S1
⋯
∑
sn
∈Sn
(∏
i∈N
qi
(si
))p(w|s)
i ∈ N
Hi
(q) =
∑
w∈W
p(w|q)hi
(w)
q1
q2
p(w3 |q) =
∑
s1
∈S1
∑
s2
∈S2
(∏
i∈N
qi
(si
))p(w3 |s)
= q1
(a1
2)q2
(a2
1 − a2
3)p(w3 |(a1
2, a2
1 − a2
3))
+q1
(a1
2)q2
(a2
1 − a2
4)p(w3 |(a1
2, a2
1 − a2
4))
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
p01
(a0
1) =
1
2
p01
(a0
2) =
1
2
७ઓུͷ૊ͷ΋ͱͰ
ʹ౸ୡ͢Δ֬཰
s
w
w3
७ઓུͷ૊Λߏ੒͢Δ
֤ϓϨΠϠʔ͕७ઓུ ʹ
ׂΓ౰ͯͨ֬཰ͷੵ
s
si

23. ߦಈઓུͷ૊ʹର͢Δ‫ظ‬଴རಘ
ߦಈઓུͷ૊ ʹରͯ͠
࢝఺͔Βऴ఺ ΁ͷ౸ୡ͢Δ֬཰Λ ͱ͢Δͱ
ϓϨΠϠʔ ͷ‫ظ‬଴རಘ͸
ྫ
ϓϨΠϠʔͷߦಈઓུΛ
ϓϨΠϠʔͷߦಈઓུΛ ͱ͢Δ
b = (b1
, ⋯, bn
)
w ∈ W p(w|b)
p(w|b) = c(w)
∏
i∈N
∏
e∈Ei
(w)
bi
(e)
i ∈ N
Hi
(b) =
∑
w∈W
p(w|b)hi
(w)
b1
b2
p(w4 |b) = c(w4)
∏
i∈N
∏
e∈Ei
bi
(e)
= p01
(a0
1)b1
(a1
2)b2
(a2
2)
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
p01
(a0
1) =
1
2
p01
(a0
2) =
1
2
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b2
u2
1
(a2
1)
b2
u2
1
(a2
2)
b2
u2
2
(a2
3)
b2
u2
2
(a2
4)
w4

24. ඪ४Խ
ల։‫ܗ‬ήʔϜ ͔Β
७ઓུͷઓུ‫ܗ‬ήʔϜ
ࠞ߹ઓུͷઓུ‫ܗ‬ήʔϜ
ߦಈઓུͷઓུ‫ܗ‬ήʔϜ
Λߏ੒Ͱ͖Δ
͜ΕΛඪ४Խͱ‫Ϳݺ‬
͜ΕʹΑΓ
͜Ε·Ͱߟ͖͑ͯͨ
ࢧ഑ઓུ
࠷ద൓Ԡઓུ
߹ཧԽՄೳઓུ
φογϡ‫ߧۉ‬ΛఆٛͰ͖Δʂ
Γ = (K, P, p, U, h)
(N, {Si
}i∈N, {Hi
}i∈N)
(N, {Qi
}i∈N, {Hi
}i∈N)
(N, {Bi
}i∈N, {Hi
}i∈N)
u1
1
u2
1
u2
2
u0
1
N
P1
P2
P2
P2
P2
a0
1
a0
2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(8, 8)
(10, 0)
(0, 10)
(6, 6)
(−6, − 6)
(0, 2)
(2, 0)
(4, 4)
a1
1
a1
2
P1
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b1
u1
1
(a1
1)
b1
u1
1
(a1
2)
b2
u2
1
(a2
1)
b2
u2
1
(a2
2)
b2
u2
2
(a2
3)
b2
u2
2
(a2
4)

25. ήʔϜཧ࿦#4*$ୈճ
ల։‫ܗ‬ήʔϜʹ͓͚Δઓུɾ‫ظ‬଴རಘ
‫׬‬
ήʔϜཧ࿦#4*$ୈճʹͭͮ͘
See you next timeʂ