https://www.youtube.com/channel/UCEr2VZ6DI4gATRtVJw49ZFw

1. ήʔϜཧ࿦#4*$ୈճ
৘ใෆ‫׬‬උήʔϜͱϕΠδΞϯήʔϜ

2. 1. ৘ใෆ‫׬‬උήʔϜΛཧղ
2. ϕΠδΞϯήʔϜΛཧղ
ຊಈըͷ໨త

3. 1. ৘ใෆ‫׬‬උήʔϜ
(1)͜Ε·ͰͷήʔϜͱͷҧ͍
(2)৘ใෆ‫׬‬උήʔϜͷఆٛ
(A)λΠϓ
(B)རಘؔ਺
(C)ϕΠδΞϯԾઆ
(D)৘ใෆ‫׬‬උήʔϜͷఆٛ
2. ϕΠδΞϯήʔϜ
(1)ϕΠδΞϯήʔϜͷఆٛ
(2)ϕΠζಉ஋Ծઆ
(3)໦ͷද‫ݱ‬
໨࣍

4. Game with incomplete information
৘ใෆ‫׬‬උήʔϜ

5. ͜Ε·ͰͷήʔϜͱͷҧ͍
৘ใ‫׬‬උήʔϜͱ৘ใෆ‫׬‬උήʔϜ
͜Ε·Ͱߟ͖͑ͯͨήʔϜͰ͸
֤ϓϨΠϠʔ͕ʮઓུͷू߹ʯʮརಘʯʮ໦ͷߏ଄ʯΛ೺Ѳͯ͠ҙࢥܾఆΛߦ͏
͜ͷΑ͏ʹ৘ใ͕‫ڞ‬༗஌ࣝͱͳ͍ͬͯΔήʔϜΛ৘ใ‫׬‬උͳήʔϜͱ͍͏
ྫ
ক‫
ع‬ғ‫Ͳͳޟ‬
Ұํ
‫࣮ࣾݱ‬ձʹ͓͍ͯ
ήʔϜͷঢ়‫گ‬Λෆ‫׬‬શʹ͔͠೺ѲͰ͖͍ͯͳ͍ঢ়‫͕͋گ‬Δ
ϓϨΠϠʔ͕ήʔϜͷ৘ใΛ೺Ѳ͍ͯ͠ͳ͍Α͏ͳήʔϜΛ৘ใෆ‫׬‬උͳήʔϜͱ͍͏
ྫ
ϙʔΧʔͳͲ
ྫ
ফඅऀͷ޷ΈͳͲ
ࠓճ͸֤ϓϨΠϠʔ͕ଞͷϓϨΠϠʔͷརಘؔ਺Λ‫׬‬શʹ͸஌Βͳ͍ঢ়‫گ‬Λߟ͑Δ
Ͳ͏ϞσϧԽ͢Δ͔ʁ
̍ʘ 'JHIU TD
'JHIU
TD
̍ʘ 'JHIU TD
'JHIU
TD
̍ʘ 'JHIU TD
'JHIU
TD
4USPOH
P1
8FBL
P1

6. ৘ใෆ‫׬‬උήʔϜͷఆٛ
λΠϓ
རಘؔ਺͕͋Δม਺Ͱܾఆ͞ΕΔͱ͢Δ͢΂ͯͷϓϨΠϠʔ͸͜ͷͷਅͷ஋Λ஌Βͳ͍
ɹ͞Βʹ͸
ͱ ‫ݸ‬ͷม਺ʹ෼ղͰ͖Δͱ͠
֤ϓϨΠϠʔ͸ ͷਅͷ஋Λ஌Δ͜ͱ͸Ͱ͖Δ͕
ɹଞͷϓϨΠϠʔͷ Λ஌Βͳ͍΋ͷͱ͢Δ
ͷΑ͏ʹෳ਺ͷ஋ͷ৔߹Λ࣋ͭ͜ͱ΋͋Γ
ΛϓϨΠϠʔͷ৘ใϕΫτϧͱ‫ Ϳݺ‬
͕औΓ͏Δ஋ͷू߹Λ Ͱද͢
͜ͷ৘ใϕΫτϧ͸‫ݸ‬ਓͷଐੑ ֶྺ
ੜ࢈ٕज़
Λද͠
·ͨ৘ใϕΫτϧ͸ࣗ෼ͷ΋ͷ͔͠஌Βͳ͍ͷͰ
‫ݸ‬ਓ৘ใͰ΋͋Δ
͜͜Ͱ͸৘ใϕΫτϧΛλΠϓͱ‫Ϳݺ‬
t t
t t = (t1
, ⋯, tn
) n i ti
tj
(j ≠ i)
ti
= (ti
1, ⋯, ti
ki) ti
i
ti
Ti

7. ৘ใෆ‫׬‬උήʔϜͷఆٛ
རಘؔ਺
རಘؔ਺͸λΠϓʹΑܾͬͯ·ΔͷͰ
Ͱද͞ΕΔ
fi
(s1
, ⋯, sn
, t1
, ⋯, tn
)

8. ৘ใෆ‫׬‬උήʔϜͷఆٛ
རಘؔ਺
རಘؔ਺͸λΠϓʹΑܾͬͯ·ΔͷͰ
Ͱද͞ΕΔ
ϕΠδΞϯԾઆ
ϓϨΠϠʔ͸ଞͷϓϨΠϠʔͷλΠϓ ͷਅͷ஋Λ༧૝͢Δ
ϓϨΠϠʔͷओ‫؍‬త༧૝͸ ‫ݸ‬ͷม਺ ͷಉ࣌֬཰෼෍ Ͱද‫͞ݱ‬Ε
ϓϨΠϠʔ͸֬཰෼෍ ʹΑΔརಘͷ‫ظ‬଴஋Λ࠷େԽ͢Δ
͸ࣗ෼ͷλΠϓ ʹґଘ͠
ͱද‫͖Ͱݱ‬Δ
fi
(s1
, ⋯, sn
, t1
, ⋯, tn
)
i t1
, ⋯, ti−1
, ti+1
, ⋯, tn
i n − 1 t1
, ⋯, ti−1
, ti+1
, ⋯, tn
pi
i pi
pi
ti
pi
(t1
, ⋯, ti−1
, ti+1
, ⋯, tn
|ti
)

9. ৘ใෆ‫׬‬උήʔϜͷఆٛ
৘ใෆ‫׬‬උήʔϜͷఆٛ
৘ใෆ‫׬‬උήʔϜ͸ Ͱද͞ΕΔ
B
͸ϓϨΠϠʔͷू߹
C
͸ϓϨΠϠʔͷߦಈͷू߹
D
͸ϓϨΠϠʔͷλΠϓͷू߹
E
͸ϓϨΠϠʔͷརಘؔ਺Ͱ͋Γ
F
͸ϓϨΠϠʔͷओ‫؍‬త༧૝Ͱ͋Γ
֤ ʹରͯ͠
௚ੵू߹ ্ͷಉ࣌֬཰෼෍
G * = (N, {Si
, Ti
, fi
, pi
}i∈N)
N
Si
i
Ti
i
fi
i fi
: S1
× ⋯ × Sn
× T1
× ⋯ × Tn
→ ℜ
pi
i ti
∈ Ti
T1
× ⋯Ti−1
× Ti+1
⋯ × Tn
pi
(t1
, ⋯, ti−1
, ti+1
, ⋯, tn
|ti
)

10. Bayesian game
ϕΠδΞϯήʔϜ

11. ϕΠδΞϯήʔϜͷఆٛ
ϕΠδΞϯήʔϜ
৘ใෆ‫׬‬උͳήʔϜΛ‫׬‬උͳήʔϜʹม‫࡯ߟͯ͠׵‬
֤ϓϨΠϠʔ͸λΠϓͷ૊શମ ্ʹ
‫ڞ‬௨ͷࣄલ֬཰෼෍ Λ‫ڞ‬༗͍ͯ͠Δͱ͢Δ
͞Βʹ֤ϓϨΠϠʔ͸͜ͷࣄલ֬཰෼෍ Λ࢖ͬͯ
ϕΠδΞϯήʔϜ͸ Ͱද͞ΕΔ
T = T1
× ⋯ × Tn
p
p
pi
(t *−i
|t*i
) =
p(t *i
, t*−i
)
∑t−i∈Ti p(t *i ,t−i)
G** = (N, {Si
, Ti
, fi
}i∈N, p)
̍ʘ 'JHIU TD
'JHIU
TD
̍ʘ 'JHIU TD
'JHIU
TD
4USPOH
4USPOH
P1
P2
T1
= (S, W) T2
= (S, W)
T = ((S, S), (S, W), (W, S), (W, W))
p = (1/12, 1/2, 1/12, 1/3)
p1
(S|S) =
p(S, S)
p(S, S) + p(S, W)
=
1/12
1/12 + 1/2
=
1
7
4USPOH
8FBL
P1
P2
̍ʘ 'JHIU TD
'JHIU
TD
8FBL
4USPOH
P1
P2
̍ʘ 'JHIU TD
'JHIU
TD
8FBL
8FBL
P1
P2

12. ϕΠζಉ஋Ծઆ
ϕΠζಉ஋Ծઆ
৘ใෆ‫׬‬උήʔϜ ͱ
ϕΠδΞϯήʔϜ ͸
ϓϨΠϠʔʹͱͬͯͷઓ্ུͷ‫͔఺؍‬Β͸ಉ஋Ͱ͋Γ
ϓϨΠϠʔͷઓུͷબ୒͸ͲͪΒͷήʔϜͰ΋
ಉܾ͡ఆϧʔϧʹै͏
Ҏ߱
͜ͷԾઆΛ࠾༻ͯ͠
৘ใෆ‫׬‬උήʔϜΛϕΠδΞϯήʔϜʹม‫ͯ͠׵‬෼ੳ͢Δ
G * = (N, {Si
, Ti
, fi
, pi
}i∈N) G** = (N, {Si
, Ti
, fi
}i∈N, p)

13. ໦ͷද‫ݱ‬
ϕΠδΞϯήʔϜ͸ҎԼͷΑ͏ͳήʔϜͷ໦Ͱ΋ද‫͖Ͱݱ‬Δɿ
P1
P2
P2
'
N
P1
P1
P1
ࣗવͱ‫ݺ‬͹ΕΔ
Ծ૝తͳϓϨΠϠʔΛஔ͘
P2
P2
P2
P2
P2
P2
4USPOH
4USPOH
8FBL
8FBL
'
'
'
T1
= (S, W) T2
= (S, W)
T = ((S, S), (S, W), (W, S), (W, W))
p = (1/12, 1/2, 1/12, 1/3)

14. ήʔϜཧ࿦#4*$ୈճ
৘ใෆ‫׬‬උήʔϜͱϕΠδΞϯήʔϜ
‫׬‬
ήʔϜཧ࿦#4*$ୈճʹͭͮ͘
See you next timeʂ