https://youtu.be/GDLHqhHuVWM

1. ήʔϜཧ࿦#4*$ୈճ
ಈతͳ৘ใෆ‫׬‬උήʔϜ

2. 1. ಈతͳ৘ใෆ‫׬‬උήʔϜΛཧղ
ຊಈըͷ໨త

3. 1. ಈతͳ৘ใෆ‫׬‬උήʔϜ
(1)ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
(2)(ࢀߟ) ෦෼ήʔϜ‫׬‬શ‫ߧۉ‬ͷ໰୊఺
(3)(෮श) ‫׬‬શϕΠδΞϯ‫ߧۉ‬
໨࣍

4. Dynamic games with Incomplete information
ಈతͳ৘ใෆ‫׬‬උήʔϜ

5. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f

6. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

7. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

8. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

9. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

10. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

11. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

12. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ

13. ϕΠδΞϯφογϡ‫ߧۉ‬ͷ໰୊఺
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
߹ཧతʁ
ϕΠδΞϯήʔϜ

14. ࢀߟ
෦෼ήʔϜ‫׬‬શ‫ߧۉ‬ͷ໰୊఺ ୈճࢀর
u1
1
u2
1
P1
P2
P2
a1
1
a1
2
a2
1
a2
2
(5, 6)
(1, 0)
(1, 3)
(2, 1)
ల։‫ܗ‬ήʔϜ ઓུ‫ܗ‬ήʔϜ
̍ʘ
a1
1
a1
2
a2
1
a2
2
a2
1
a2
2
a1
3
(3, 5)
a1
3
φογϡ‫͔ͭߧۉ‬෦෼ήʔϜ‫׬‬શ‫ߧۉ‬
߹ཧత͔ʁ
ෳ਺ͷ఺Λ‫ؚ‬Ή৘ใू߹্Ͱ
ࣗ෼͕Ͳͷ఺ʹ͍Δ͔ͱ͍͏͔֬Β͠͞Λಋೖ͢Δ

15. ෮श
‫׬‬શϕΠδΞϯ‫ߧۉ‬ͷఆٛ
‫׬‬શϕΠδΞϯ‫ߧۉ‬
ઓུͷ૊ ͱ৴೦ͷମ‫ܥ‬ ͷ૊ Ͱ
͕ ͷ΋ͱͰஞ࣍߹ཧతͰ͋Γ
͕ ʹ੔߹తͰ͋Δ΋ͷΛ
ऑ‫׬‬શϕΠδΞϯ‫͏͍ͱߧۉ‬
ߦಈઓུͷஞ࣍߹ཧੑ
ల։‫ܗ‬ήʔϜ ʹ͓͍ͯ
৴೦ͷମ‫ܥ‬ ͕༩͑ΒΕ͍ͯΔͱ͢Δ͜ͷͱ͖
ઓུͷ૊ ͕
ϓϨΠϠʔͷ৘ใू߹ ʹ͓͍ͯҎԼΛຬͨ͢ͱ͖
͸৴೦ͷମ‫ܥ‬ ͷ΋ͱͰ৘ใू߹ ʹ͓͍ͯஞ࣍߹ཧతͰ͋Δͱ͍͏
͕೚ҙͷϓϨΠϠʔͷ೚ҙͷ৘ใू߹ ʹ͓͍ͯஞ࣍߹ཧతͰ͋Δ৔߹
͸৴೦ͷମ‫ܥ‬ ͷ΋ͱͰஞ࣍߹ཧతͰ͋Δͱ͍͏
৴೦ͷମ‫ͱܥ‬੔߹ੑ
ల։‫ܗ‬ήʔϜ ʹ͓͍ͯ
ઓུͷ૊ ͕༩͑ΒΕ͍ͯΔͱ͢Δ͜ͷͱ͖
৴೦ͷମ‫ܥ‬ ͕
೚ҙͷϓϨΠϠʔͷ೚ҙͷ৘ใू߹ ʹ͓͍ͯ
Ͱ͋Ε͹
͢΂ͯͷ ͷ఺ ʹ͍ͭͯ
ͱͳΔͱ͖
͸ઓུͷ૊ ʹ͓͍ͯ੔߹తͰ͋Δͱ͍͏
b μ (b, μ) b μ μ b
Γ μ b = (b1
, ⋯, bn
) i ui
l
b μ ui
l
Hi
(ui
l, μ, (bi,ui
l, b−i,ui
l)) ≥ Hi
(ui
l, μ, (b′i,ui
l, b−i,ui
l)), ∀b′i,ui
l ∈ Bi,ui
l
b i ui
l b μ
Γ b = (b1
, ⋯, bn
) μ i ui
l
Prob(ui
l |b) 0 ui
l x*
μ(x*) =
Prob(x*|b)
∑x∈ui
l
Prob(x|b)
μ b
x0
x1
x2
p =
1
4
/(
1
4
+
1
3
) =
3
7
1 − p
1
4
1
3
5
12
p

16. ‫׬‬શϕΠδΞϯ‫ߧۉ‬
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
৘ใू߹ ʹ͓͚Δ৴೦Λ ͱ͢Δ
ΛબΜͩͱ͖ͷ‫ظ‬଴རಘ
ΛબΜͩͱ͖ͷ‫ظ‬଴རಘ
͜ΕΑΓ
ͲΜͳ৴೦Λͱͬͨͱͯ͠΋
ΛબͿ͜ͱ͕࠷ద
͢ͳΘͪ
ΛબͿΑ͏ͳߦಈઓུ͸ஞ࣍߹ཧੑΛຬͨ͢
ΛબͿΑ͏ͳߦಈઓུ͸ஞ࣍߹ཧੑΛຬͨ͞ͳ͍
u2
2 (r, 1 − r)
e 2r + 1 − r = r + 1
f 1r + 0(1 − r) = r
e
e
f
r
1 − r
u2
2
u2
1

17. ‫׬‬શϕΠδΞϯ‫ߧۉ‬
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
ϓϨΠϠʔ͕ Λͱ͍ͬͯΔͱ͖ͷ
ʹ͓͚Δ੔߹తͳ৴೦͸
ʹ͓͚Δ੔߹తͳ৴೦͸
a − a
u2
1 (
1
2
,
1
2
)
u2
2 (r, 1 − r), ∀r ∈ [0, 1]
r
1 − r
u2
2
u2
1
1
2
1
2

18. ‫׬‬શϕΠδΞϯ‫ߧۉ‬
ల։‫ܗ‬ද‫ݱ‬
a
N
c
1
1
2
2
ࣗવ
t1
1
(3, 3)
(0, 1)
(−2, 2)
1
2
1
2
٬‫཰֬؍‬
t1
2
a
b
b
d
(2, 1)
2
(−1, 1)
(−2, 0)
(0, 3)
(1, 3)
2
c
d
e
f
e
f
̍ʘ DF DG EF EG
BB
BC
CB
CC
ϕΠδΞϯήʔϜ
r
1 − r
1
2
1
2
u2
2
u2
1
1
1
u1
1
u1
2

19. ήʔϜཧ࿦#4*$ୈճ
ಈతͳ৘ใෆ‫׬‬උήʔϜ
‫׬‬
ήʔϜཧ࿦#4*$ୈճʹͭͮ͘
See you next timeʂ