https://youtu.be/sE8EOSS2PdI

1. ήʔϜཧ࿦#4*$ୈճิ଍
φογϡ‫ͱߧۉ‬ϕΠδΞϯφογϡ‫ߧۉ‬ͷؔ܎

2. 1. ϕΠδΞϯφογϡ‫ ͱߧۉ‬
φογϡ‫͕ߧۉ‬ಉ஋Ͱ͋Δ͜ͱΛཧղ
ຊಈըͷ໨త

3. 1. ϕΠδΞϯφογϡ‫ͱߧۉ‬φογϡ‫ߧۉ‬ͷಉ஋ੑ
(1)ϕΠδΞϯφογϡ‫ͱߧۉ‬φογϡ‫ߧۉ‬
(2)ূ໌
໨࣍

4. ϕΠδΞϯφογϡ‫ͱߧۉ‬φογϡ‫ߧۉ‬
ϕΠδΞϯφογϡ‫ߧۉ‬
ઓུͷ૊ ʹ͓͍ͯ
֤ϓϨΠϠʔͷ֤λΠϓ ʹ͍ͭͯ
ͷ༩͑Δߦಈ͕ଞͷϓϨΠϠʔͷ֤λΠϓͷߦಈʹର͢Δ࠷ద൓Ԡͱͳ͍ͬͯΔͱ͖
ͭ·Γ
͢΂ͯͷ ͱͷ͢΂ͯͷλΠϓ ʹରͯ͠
ͱͳ͍ͬͯΔͱ͖
ΛϕΠδΞϯφογϡ‫͏͍ͱߧۉ‬
φογϡ‫ߧۉ‬
ϕΠδΞϯήʔϜʹ͓͚Δઓུͷ૊ ʹ͓͍ͯ
͢΂ͯͷ ʹରͯ͠
ͱͳ͍ͬͯΔͱ͖
Λφογϡ‫͏͍ͱߧۉ‬
x* = (x*1
, ⋯, x*n
) i ti
x*i
i ∈ N i ti
∑
t−1
∈T−1
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ≥
∑
t−1
∈T−1
fi
(si
, x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ∀si
∈ Si
x* = (x*1
, ⋯, x*n
)
x* = (x*1
, ⋯, x*n
) i ∈ N
∑
t∈T
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
) ≥
∑
t∈T
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
) ∀xi
∈ Xi
x* = (x*1
, ⋯, x*n
)
৚݅෇‫ظ‬଴རಘ
‫ظ‬଴རಘ

5. ূ໌
ϕΠδΞϯφογϡ‫ͱߧۉ‬φογϡ‫ߧۉ‬ͷಉ஋ੑ
ϕΠδΞϯφογϡ‫͋Ͱߧۉ‬Δ͜ͱ͸
φογϡ‫͋Ͱߧۉ‬ΔͨΊͷඞཁे෼৚݅Ͱ͋Δ
ɹ
ϕΠδΞϯφογϡ‫͋Ͱߧۉ‬Ε͹φογϡ‫ͳͱߧۉ‬Δ͜ͱΛࣔ͢
ϕΠδΞϯφογϡ‫ߧۉ‬ ͱ͢Δ೚ҙͷϓϨΠϠʔͱ೚ҙͷઓུ ΛબͿ
͢΂ͯͷϓϨΠϠʔʹରͯ͠
ϕΠζͷެ͔ࣜΒҎԼ͕੒Γཱͭ
·ͨ
͸ϕΠδΞϯφογϡ‫͔ͩߧۉ‬Β
ΑΓҎԼͷࣜ΋ຬͨ͢
x* = (x*1
, ⋯, x*n
) i xi
i
pi
(t−i
|ti
) =
p(ti
, t−i
)
∑t−i∈Ti p(ti, t−i)
⇔ p(ti
, t−i
) = pi
(t−i
|ti
)
∑
t−i
∈T
i
p(ti
, t−i
)
x* = (x*1
, ⋯, x*n
)
∑
t−1
∈T−1
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ≥
∑
t−1
∈T−1
fi
(si
, x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ∀si
∈ Si
∑
t−1
∈T−1
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ≥
∑
t−1
∈T−1
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ͷ༩͑Δߦಈʹରͯ͠΋੒Γཱͭ
xi

6. ূ໌
ϓϨΠϠʔͷ‫ظ‬଴རಘʹ͍ͭͯ
T = ((SW, SW), (HP, SW), (SW, HP), (HP, HP))
∑
t∈T
f1
(x1
(t1
), x2
(t2
), t1
, t2
)p(t1
, t2
)
= f1
(x1
(SW), x2
(SW), SW, SW)p(SW, SW) + f1
(x1
(SW), x2
(HP), SW, HP)p(SW, HP)
+f1
(x1
(HP), x2
(SW), HP, SW)p(HP, SW) + f1
(x1
(HP), x2
(HP), HP, HP)p(HP, HP)
=
∑
t2
∈T2
f1
(x1
(SW), x2
(t2
), SW, t2
)p(SW, t2
)
+
∑
t2
∈T2
f1
(x1
(HP), x2
(t2
), HP, t2
)p(HP, t2
)
=
∑
t1
∈T1
∑
t2
∈T2
f1
(x1
(t1
), x2
(t2
), t1
, t2
)p(t1
, t2
)
̍ʘ 4 )
4 ̎
)
̍
̍ʘ 4 )
4
)
48
48
P1
P2 )1
48
P1
P2
̍ʘ 4 )
4 ̎
)
̍
̍ʘ 4 )
4
)
48
)1
P1
P2 )1
)1
P1
P2
p1
p2
p3
p4

7. ূ໌
ϕΠδΞϯφογϡ‫͋Ͱߧۉ‬Ε͹φογϡ‫ͳͱߧۉ‬Δ͜ͱΛࣔ͢
͜ΕΑΓ‫ظ‬଴རಘ͸
ͱͳΓ
೚ҙͷ Λߟ͍͑ͯͨͷͰ
͸ ʹର͢Δ࠷ద൓ԠͰ͋Γ
͢΂ͯͷϓϨΠϠʔͰ੒ΓཱͭͷͰ
͸φογϡ‫͋Ͱߧۉ‬Δ
∑
t∈T
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
)
=
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
))
=
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
)
∑
t−i
∈T
i
p(ti
, t−i
))
≥
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
)
∑
t−i
∈T
i
p(ti
, t−i
))
=
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
)) =
∑
t∈T
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
)
xi
x*i
x*−i
i
x* = (x*1
, ⋯, x*n
)
p(ti
, t−i
) = pi
(t−i
|ti
)
∑
t−i
∈T
i
p(ti
, t−i
)
৚݅෇‫ظ‬଴རಘ
∑
t−1
∈T−1
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
) ≥
∑
t−1
∈T−1
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
)

8. ূ໌
φογϡ‫͋Ͱߧۉ‬Ε͹ϕΠδΞϯφογϡ‫ͳͱߧۉ‬Δ͜ͱΛࣔ͢
φογϡ‫ߧۉ‬ ͱ͢Δഎཧ๏Λ࢖͏ࠓ
͜ͷઓུͷ૊͕ϕΠδΞϯφογϡ‫͢ͱ͍ͳͰߧۉ‬Δͱ
͋ΔϓϨΠϠʔͷ͋ΔλΠϓ
͋Δߦಈ ʹରͯ͠
͕੒Γཱͭ
͜͜ͰϓϨΠϠʔͷઓུΛ
ʹΑͬͯఆٛ͢Δͱ
Ҏ֎ͷλΠϓ͸ ͱ Ͱ‫ظ‬଴རಘ͸౳͍ͨ͠Ί
ͱͳΓ
͕φογϡ‫͋Ͱߧۉ‬Δ͜ͱʹ൓͢Δ
x* = (x*1
, ⋯, x*n
)
i t̄i
si
∑
t−1
∈T−1
fi
(x*i
(t̄i
), x*−i
(t−i
), t̄i
, t−i
)pi
(t−i
|t̄i
)
∑
t−1
∈T−1
fi
(si
, x*−i
(t−i
), t̄i
, t−i
)pi
(t−i
|t̄i
)
i xi
(ti
) =
{
si
(ti
= t̄i
)
x*i
(ti
) (ti
≠ t̄i
)
t̄i
xi
x*i
∑
t∈T
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
) =
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
)) =
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(x*i
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
)
∑
t−i
∈T
i
p(ti
, t−i
))
∑
ti
∈Ti
(
∑
t−i
∈T−i
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)pi
(t−i
|ti
)
∑
t−i
∈T
i
p(ti
, t−i
)) =
∑
t∈T
fi
(xi
(ti
), x*−i
(t−i
), ti
, t−i
)p(ti
, t−i
)
x* = (x*1
, ⋯, x*n
)

9. ήʔϜཧ࿦#4*$ୈճิ଍
φογϡ‫ͱߧۉ‬ϕΠδΞϯφογϡ‫ߧۉ‬ͷؔ܎
‫׬‬
ήʔϜཧ࿦#4*$ୈճʹͭͮ͘
See you next timeʂ