3. ήʔϜ
ϓϨΠϠʔͷू߹
ϓϨΠϠʔ ͷߦಈͷू߹
ϓϨΠϠʔ ͷརಘؔ ͱͯ͠
܁Γฦ͠ήʔϜʹ͓͚Δઓུ
ͱͯ͠
ͱ͠
ͱ͢Δ
͜͜Ͱ
Λ ճ·Ͱͷཤྺͱ͍͏
ϓϨΠϠʔ ͷ ճͷߦಈ
ཤྺ Λͱʹܾఆ͞ΕΔ
͢ͳΘͪ Ͱ༩͑ΒΕΔ
͜ΕΑΓ܁Γฦ͠ήʔϜʹ͓͚ΔϓϨΠϠʔ ͷ७ਮઓུ Ͱ༩͑ΒΕΔ
ϓϨΠϠʔ ͷ७ਮઓུͷू߹Λ ͱ͠
ϓϨΠϠʔશମͷઓུͷͷू߹Λ Ͱද͢
G = (N, {Si
}i∈N, {fi
}i∈N)
N
Si
i
fi
i S = S1
× ⋯ × Sn
fi
: S → ℜ
S = S1
× ⋯ × Sn
St−1 =
t−1
S × ⋯ × S S0 = {∅}
ht−1 = (s1, ⋯, st−1) ∈ St−1 t − 1
i t ht−1 xi
t : St−1 → Si
i xi
= (xi
t)T
t=1
i XTi
XT
= XT1
× ⋯ × XTn
ήʔϜ܁Γฦ͠ήʔϜʹ͓͚Δઓུ
܁Γฦ͞ΕΔήʔϜͷ͜ͱ
8. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
9. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
10. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
(−6 + 0δ, − 6 + 0δ)
11. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
(−6 + 0δ, − 6 + 0δ)
(−6 + 2δ, − 6 + 2δ)
12. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
(−6 + 0δ, − 6 + 0δ)
(−6 + 2δ, − 6 + 2δ)
13. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
(−6 + 0δ, − 6 + 0δ)
(−6 + 2δ, − 6 + 2δ)
(0 + (−6)δ, 0 + (−6)δ)
14. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
(−6 + 0δ, − 6 + 0δ)
(−6 + 2δ, − 6 + 2δ)
(0 + (−6)δ, 0 + (−6)δ)
(0 + 0δ, 0 + 0δ)
15. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−6 + (−6)δ, − 6 + (−6)δ)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
H
L
(−6 + 0δ, − 6 + 0δ)
(−6 + 0δ, − 6 + 0δ)
(−6 + 2δ, − 6 + 2δ)
(0 + (−6)δ, 0 + (−6)δ)
(0 + 0δ, 0 + 0δ)
(0 + 0δ, 0 + 0δ)
(0 + 2δ, 0 + 2δ)
(0 + (−6)δ, 0 + (−6)δ)
(0 + 0δ, 0 + 0δ)
(0 + 0δ, 0 + 0δ)
(0 + 2δ, 0 + 2δ)
(2 + (−6)δ, 2 + (−6)δ)
(2 + 0δ, 2 + 0δ)
(2 + 0δ, 2 + 0δ)
(2 + 2δ, 2 + 2δ)
16. ׂҾҼࢠ ͱ͠
֤ۀاͷׂҾརಘΛٻΊΑ
δ = 0.5
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
17. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
18. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
̍ʘ ) -
)
-
19. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
̍ʘ ) -
)
-
20. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
̍ʘ ) -
)
-
21. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
̍ʘ ) -
)
-
22. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
23. ෦ήʔϜશߧۉΛٻΊΑ
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
ใू߹
ۀا
P1
ۀا
P2
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
̍ʘ ) -
)
-
ॖήʔϜʹ͓͚Δརಘද
(−5, − 5)
(1, 1)
(1, 1)
(3, 3)
24. ෦ήʔϜશߧۉΛٻΊΑ
෦ήʔϜશߧۉ
(x1
1, (x1
2,1, x1
2,2, x1
2,3, x1
2,4)) = (L, (L, L, L, L))
(x2
1, (x2
2,1, x2
2,2, x2
2,3, x2
2,4)) = (L, (L, L, L, L))
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
26. ෦ήʔϜશߧۉΛٻΊΑ
෦ήʔϜશߧۉ
(x1
1, (x1
2,1, x1
2,2, x1
2,3, x1
2,4)) = (L, (L, L, L, L))
(x2
1, (x2
2,1, x2
2,2, x2
2,3, x2
2,4)) = (L, (L, L, L, L))
ճ܁Γฦ͠ՉࢢήʔϜ
̍ʘ ) -
)
-
P1
(−9, − 9)
H
P2
P2
P1
P2
P2
P1
P2
P2
P1
P2
P2
P2
P2
P1
(−6, − 6)
H
H
H
L
L
L
H
L
L
H
L
H
L
H
L
(−6, − 6)
(−5, − 5)
H
L
(−3, − 3)
(0, 0)
H
L
(1, 1)
H
L
(−3, − 3)
(0, 0)
H
L
(0, 0)
(1, 1)
H
L
(−1, − 1)
(2, 2)
H
L
(2, 2)
(3, 3)
H
L
(0, 0)
φογϡߧۉෳ͋Δ
ߧۉύεʹͳ͍෦ήʔϜʹ͓͚ΔߦಈΛม͑ͨઓུΛߟ͑ͯΈΔ
ྫ͑ۀاͷઓུΛ -
-
)
-
-
ͱͯ͠
ۀاͷઓུ -
-
-
-
-
ʹରͯ͠࠷ద རಘ࠷େ
Ͱ͋Δ
Ұํ
ۀا ͕ۀا-
-
)
-
-
Λͱ͍ͬͯΔͱ͖
-
-
-
-
-
ΛऔΔͷ࠷దͱͳ͍ͬͯΔ
27. ఆཧ
ήʔϜ͕ͨͩҰͭͷφογϡߧۉ Λͪ
ͯ͢ͷϓϨΠϠʔ ͷߧۉརಘ͕
ϛχϚοΫεརಘ ʹ͍͠ͱ͢Δ͜ͷͱ͖
ҙͷ ʹରͯ͠
ճ܁Γฦ͠ήʔϜʹ͓͚Δφογϡߧۉ ͨͩҰͭଘࡏ͠
ߦಈͷ Λ༩͑Δ
ϛχϚοΫεߦಈͱϛχϚοΫεརಘ
ήʔϜ ʹ͓͍ͯ
Λຬͨ͢ϓϨΠϠʔ Ҏ֎ͷߦಈͷ Λ ʹର͢ΔϛχϚοΫεߦಈͱ͍͏
͜ͷ ΛϛχϚοΫεརಘΛ͍͍
Ͱද͢ ΛϛχϚοΫεͱ͍͏
s* i ∈ N
vi
T = 1,2,⋯
T x* s(x*) = (
T
s*, s*, ⋯, s*)
G
max
si
fi
(si
, ̂
s−i
) = min
s−i
max
si
fi
(si
, s−i
)
i ̂
s−i
i
max
si
fi
(si
, ̂
s−i
) vi
v = (v1
, ⋯, vn
)
ఆཧ
̍ʘ ) -
)
-
͕݅૿͑ͯΔ
ࠓճͷήʔϜʹ͓͚ΔϛχϚοΫεརಘۀاۀا
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