2人ゲームの混合戦略ナッシュ均衡：ラベル法

1. ήʔϜཧ࿦#4*$ԋश
ਓήʔϜͷࠞ߹ઓུφογϡ‫ߧۉ‬ɿϥϕϧ๏

2. ࠞ߹ઓུφογϡ‫ߧۉ‬ͷఆٛ
ϥϕϧ๏
ਓήʔϜͷφογϡ‫ߧۉ‬

3. ࠞ߹ઓུφογϡ‫ߧۉ‬
ϓϨΠϠʔ Ҏ֎ͷࠞ߹ઓུΛ ͱ͠‫ݻ‬ఆ͢Δ
Λຬͨ͢ͱ͖ ͸ ʹର͢Δ࠷ద൓Ԡઓུͱ͍͏
ઓུͷ૊ ͕ࠞ߹ઓུφογϡ‫͋Ͱߧۉ‬Δͱ͸
͢΂ͯͷϓϨΠϠʔʹରͯ͠
Λຬͨ͢ͱ͖Λ͍͏
ήʔϜཧ࿦#4*$ୈճࢀর
i p−i
∈ P−i
Fi
(p*i
, p−i
) ≥ Fi
(pi
, p−i
), ∀pi
∈ Pi
p*i
p−i
(p*1
, ⋯, p*n
) ∈ P
Fi
(p*i
, p*−i
) ≥ Fi
(pi
, p*−i
), ∀pi
∈ Pi

4. ϥϕϧ๏
γϟʔϓϨΠͷϥϕϧ๏
ਓήʔϜʹ͓͍ͯ ͭҎ্ͷ७ઓུΛ΋ͭ৔߹͸
ҎԼͷϥϕϧ๏Λ༻͍ͯ‫ٻ‬ΊΔͱྑ͍
ϓϨΠϠʔ਺͸ ͢ͳΘͪ ͱ͢Δ
७ઓུͷू߹
རಘߦྻ
ࠞ߹֦େ͞Εͨઓུͷू߹
ఆٛα
ポ
ʔτ
αϙʔτͱ͸ ༩͑ΒΕͨࠞ߹ઓུͷ΋ͱͰਖ਼ͷ֬཰ׂ͕Γ౰͍ͨͬͯΔઓུͷू߹Ͱ͋Δ
プ
ϨΠϠʔͷ೚ҙͷࠞ߹ઓུ ʹରͯ͠ ͷα
ポ
ʔτ Λ࣍ͷΑ͏ʹఆٛ͢Δ
ϓϨΠϠʔʹ͍ͭͯ΋αϙʔτΛఆٛ͠ Ͱද͠
ʢྫʣϓϨΠϠʔͷࠞ߹ઓུ Ͱ͋Ε͹
ϓϨΠϠʔͷࠞ߹ઓུ Ͱ͋Ε͹
ϓϨΠϠʔͷࠞ߹ઓུ Ͱ͋Ε͹
N = {1, 2}
I = {1,2,⋯, m} J = {m + 1,m + 2,⋯, m + n}
A = (aij; i ∈ I, j ∈ J) B = (bij; i ∈ I, j ∈ J)
S = {(s1, s2, ⋯, sm) ∈ Rm
+ |
m
∑
i=1
si = 1} T = {(tm+1, tm+2, ⋯, tm+n) ∈ Rn
+ |
m+n
∑
j=m+1
tj = 1}
s = (s1, ⋯, sm) ∈ S s I(s) I(s) = {i ∈ I|si ≠ 0}
J(t) J(t) = {j ∈ J|tj ≠ 0}
s = (1/2, 1/2, 0) I(s) = {1,2}
s = (1, 0, 0) I(s) = {1}
s = (0, 0, 1) I(s) = {3}
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5
s3
t6

5. プ
ϨΠϠʔͷ֤७ઓུ ʹରͯ͠ɼ
プ
ϨΠϠʔͷࠞ߹ઓུ͔ΒͳΔू߹ Λ࣍ͷΑ͏ʹఆٛ
͜ͷू߹ʹ‫·ؚ‬ΕΔࠞ߹ઓུʹର͠ ϓϨΠϠʔʹͱͬͯ ͕࠷ద൓Ԡ
͸ۭͷ৔߹΋͋Δ·ͨ Ͱ͋Δɻ
ྫʣϓϨΠϠʔ͕ ɿ
ϓϨΠϠʔ͕ ɿ
ϓϨΠϠʔ͕ ɿ
j ∈ J
Sj
Sj
= {s ∈ S|
m
∑
i=1
bijsi = max
k∈J
m
∑
i=1
biksi}
j ∈ J
Sj
S =
⋃
j∈J
Sj
4 1 × s1 + 0 × s2 + 0 × s3 = s1
5 0 × s1 + 1 × s2 + 0 × s3 = s2
6 0 × s1 + 0 × s2 + 1 × s3 = s3
S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3} S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3}
S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
ઓུ‫ܗ‬ήʔϜ
ʘ
ϥϕϧ๏
s1
s2
t4 t5
s3
t6
ϓϨΠϠʔ͕
७ઓུ Λऔͬͨͱ͖
‫ظ‬଴஋͕࠷େ
j
s3
s2
s1
̍
̍
̍
̌
S4

6. プ
ϨΠϠʔͷ७ઓུ ʹରͯ͠ɼू߹ Λ࣍ͷΑ͏ʹఆٛ
ϓϨΠϠʔͷࠞ߹ઓུ ͷϥϕϧΛ
ྫʣϓϨΠϠʔͷࠞ߹ઓུ ͷϥϕϧ͸
i ∈ I Si
Si
= {s ∈ Rm
+ |
m
∑
k=1
sk ≤ 1, si = 0}
s ∈ S L(s) = {k ∈ I ∪ J|s ∈ Sk
}
(s1, s2, s3) = (1/2, 1/2, 0)
S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1} S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1}
S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3} S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
L((1/2, 1/2, 0)) = {3,4,5}
ઓུ‫ܗ‬ήʔϜ
ʘ
ϥϕϧ๏
s1
s2
t4 t5
s3
t6

7. プ
ϨΠϠʔͷ֤७ઓུ ʹରͯ͠ɼ
プ
ϨΠϠʔͷࠞ߹ઓུ͔ΒͳΔू߹ Λ࣍ͷΑ͏ʹఆٛ
プ
ϨΠϠʔͷ७ઓུ ʹରͯ͠ɼू߹ Λ
ϓϨΠϠʔͷࠞ߹ઓུ ͷϥϕϧΛ
ྫʣϓϨΠϠʔͷࠞ߹ઓུ ͷϥϕϧ͸
i ∈ I
Ti
Ti
= {t ∈ T|
m+n
∑
j=m+1
aijtj = max
k∈I
m+n
∑
j=m+1
akjtj}
j ∈ J Tj
Tj
= {t ∈ Rn
+ |
m+n
∑
k=m+1
tk ≤ 1, tj = 0}
t ∈ T L(t) = {k ∈ I ∪ J|t ∈ Tk
}
(t4, t5, t6) = (1, 0, 0)
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1} T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1}
T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4} T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
L((1, 0, 0)) = {3, 5, 6}
ઓུ‫ܗ‬ήʔϜ
ʘ
ϥϕϧ๏
s1
s2
t4 t5
s3
t6
ϓϨΠϠʔ͕
७ઓུ Λऔͬͨͱ͖
‫ظ‬଴஋͕࠷େ
i

8. ࠞ߹ઓུͷϥϕϧΛ Ͱఆٛ͢Δ
ྫʣ
ϓϨΠϠʔͷࠞ߹ઓུ
ϓϨΠϠʔͷࠞ߹ઓུ
ఆཧ
ࠞ߹ઓུ ͕ઓུ‫ܗ‬ਓήʔϜͷ‫͋Ͱ఺ߧۉ‬ΔͨΊͷඞཁे෼৚݅͸
ɾɾɾʢˎʣ
Ͱ͋Δ͜ͱͰ͋Δ
ʢˎʣͱͳΔͱ͖ࠞ߹ઓུ ͸‫׬‬શϥϕϧΛ࣋ͭͱ͍͏
L(s, t) = L(s) ∪ L(t)
(s1, s2, s3) = (1/2, 1/2, 0)
(t4, t5, t6) = (1, 0, 0)
L((1/2, 1/2, 0), (1, 0, 0)) = {3,4,5} ∪ {3,5,6} = {3,4,5.6}
(s, t)
L(s, t) = I ∪ J
(s, t)
ઓུ‫ܗ‬ήʔϜ
ʘ
ϥϕϧ๏
s1
s2
t4 t5
s3
t6

9. ӈͷήʔϜʹ͓͚Δࠞ߹ઓུφογϡ‫ߧۉ‬Λ‫ٻ‬ΊΑ
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5
s3
t6

10. S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1}
S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1} S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3}
S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5
s3
t6
s3
s2
s1
̍
̍
̍
̌
s2
s3
s1
S6

11. S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1}
S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1} S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3}
S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5
s3
t6
S4
s3
s1 s2
S6
s3
s2
s1
̍
̍
̍
̌
s2
s3
s1
S5
S5
S2
S1
S3

12. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1}
S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1} S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3}
S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
{4},
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
S4
s3
s1 s2
S6
S5
S2
S1
S3
s3

13. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1}
S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1} S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3}
S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
{4}, {5}, {6}, {3,4},
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
S4
s3
s1 s2
S6
S5
S2
S1
S3
s3

14. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1}
S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1} S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3}
S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
{4}, {5}, {6}, {3,4}, {3,5}, {2,4}, {2,6} {1,6} {1,5} {4,5} {4,6} {5,6}
{4,5,6} {2,4,6} {1,5,6} {3,4,5}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
S4
s3
s1 s2
S6
S5
S2
S1
S3
s3

15. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
S1
= {s ∈ S|s1 = 0, s2 + s3 ≤ 1} S2
= {s ∈ S|s2 = 0, s1 + s3 ≤ 1}
S3
= {s ∈ S|s3 = 0, s2 + s3 ≤ 1} S4
= {s ∈ S|s1 ≥ s2 and s1 ≥ s3}
S5
= {s ∈ S|s2 ≥ s1 and s2 ≥ s3} S6
= {s ∈ S|s3 ≥ s1 and s3 ≥ s2}
{4}, {5}, {6}, {3,4}, {3,5}, {2,4}, {2,6} {1,6} {1,5} {4,5} {4,6} {5,6}
{4,5,6} {2,4,6} {1,5,6} {3,4,5} {2,3,4} {1,2,6} {1,3,5}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
S4
s3
s1 s2
S6
S5
S2
S1
S3
s3

16. T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
t6
t5
t4
̍
̍
̍
̌
s3
T1
(
1
3
,
1
2
,
1
6 )

17. T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
t6
t5
t4
̍
̍
̍
̌
s3
T2
(
1
3
,
1
2
,
1
6 )

18. T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
t6
t5
t4
̍
̍
̍
̌
s3
T3
(
1
3
,
1
2
,
1
6 )

19. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
{1} {2} {3}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
T3
T2
T1
s3

20. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
{1} {2} {3} {3,5} {3,6} {2,4} {2,5} {1,4} {1,6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
T3
T2
T1
s3

21. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
{1} {2} {3} {3,5} {3,6} {2,4} {2,5} {1,4} {1,6} {1,2} {1,3} {2,3}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
T3
T2
T1
s3

22. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
T4
= {t ∈ T|t4 = 0, t5 + t6 ≤ 1} T5
= {t ∈ T|t5 = 0, t4 + t6 ≤ 1}
T6
= {t ∈ T|t6 = 0, t4 + t5 ≤ 1} T1
= {t ∈ T|t5 ≥ t4 + t6 and t5 + t6 ≥ 2t4}
T2
= {t ∈ T|t4 + t6 ≥ t5 and 2t6 ≥ t4} T3
= {t ∈ T|2t4 ≥ t5 + t6 and t4 ≥ 2t6}
{1} {2} {3} {3,5} {3,6} {2,4} {2,5} {1,4} {1,6} {1,2} {1,3} {2,3}
{1,2,3} {1,2,4} {1,3,6} {1,4,6} {2,3,5} {2,4,5} {3,5,6}
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
t6
t4 t5
T5
T4
T6
T3
T2
T1
s3

23. ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
ϓϨΠϠʔͷࠞ߹ઓུͷՄೳͳϥϕϧ͸
ͱͳΔ૊Έ߹ΘͤΛ୳͢
૬ख͕ߴʑ̏ͭͷઓུΛ‫ؚ‬Ήϥϕϧ͔͠ͳ͍ͷͰ
গͳ͘ͱ΋ࣗ෼ͷϥϕϧʹ͸ͭͷઓུ͕‫·ؚ‬Ε͍ͯΔ͜ͱ͕ඞཁʹͳΔ
ͱ ͷ૊Έ߹ΘͤͷΈ ‫׬‬શϥϕϧͱͳΔ
͸ӈਤ͔Β
͸ӈਤ͔Β
{4}, {5}, {6}, {3,4}, {3,5}, {2,4}, {2,6} {1,6} {1,5} {4,5} {4,6} {5,6}
{4,5,6} {2,4,6} {1,5,6} {3,4,5} {2,3,4} {1,2,6} {1,3,5}
{1} {2} {3} {3,5} {3,6} {2,4} {2,5} {1,4} {1,6} {1,2} {1,3} {2,3}
{1,2,3} {1,2,4} {1,3,6} {1,4,6} {3,5,6} {2,3,5} {2,4,5}
L(s, t) = I ∪ J = {1,2,3,4,5,6}
{4,5,6} {1,2,3}
{4,5,6} s =
(
1
3
,
1
3
,
1
3)
{1,2,3} t =
(
1
3
,
1
2
,
1
6)
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5 t6
s3
S4
s3
s1 s2
S6
S5
S2
S1
S3
t6
t4 t5
T5
T4
T6
T3
T2
T1

24. ӈͷήʔϜʹ͓͚Δࠞ߹ઓུφογϡ‫ߧۉ‬Λ‫ٻ‬ΊΑ
ղ౴ɿ
ͷ૊Έ߹Θ͕ͤφογϡ‫ߧۉ‬
s =
(
1
3
,
1
3
,
1
3)
t =
(
1
3
,
1
2
,
1
6)
ਓήʔϜͷφογϡ‫ߧۉ‬
ઓུ‫ܗ‬ήʔϜ
ʘ
s1
s2
t4 t5
s3
t6

25. ήʔϜཧ࿦#4*$ԋश
ਓήʔϜͷࠞ߹ઓུφογϡ‫ߧۉ‬ɿϥϕϧ๏