https://youtu.be/C7aWQt-J9XI

1. ήʔϜཧ࿦#4*$ԋश
ਓަবήʔϜ

2. ަব໰୊ͷఆٛ ෮श
ަবղ͕ຬͨ͢΂͖ͭͷެཧ ෮श
ԋश

3. ަব໰୊ͷఆٛ
ఆٛɿަব໰୊͸
࣮‫ݱ‬Մೳू߹ɿ
ަবͷෆҰக఺ɿ
ͷ૊ ʹΑͬͯఆٛ͞ΕΔ
Ծఆ
w ͸࣍‫ۭؒ਺࣮ݩ‬ ͷίϯύΫτͰತͳ෦෼ू߹
w
w ͷ఺ ͕ଘࡏͯ͠
U
d = (d1
, d2
)
(U, d)
U ℜ2
d ∈ U
U u = (u1
, u2
) ui
di
(i = 1, 2)
0
u2
u1
(d1
, d2
) = (20, 20)
U
100
100

4. ަবղ͕ຬͨ͢΂͖ͭͷެཧ
ύϨʔτ࠷దੑ
͢΂ͯͷ ʹରͯ͠ Ͱ
গͳ͘ͱ΋ͭͷ ʹରͯ͠
Ͱ͋Δ ͷ఺ ͸ଘࡏ͠ͳ͍
ରশੑ
ަব໰୊ ͕ରশͳΒ͹
ˎަব໰୊͕ରশͰ͋Δͱ͸
ͳΒ͹
ਖ਼࣍ม‫͔׵‬Βͷಠཱੑ
ަব໰୊ ͕ަব໰୊ ͔Βޮ༻ͷਖ਼࣍ม‫׵‬ ʹΑͬͯಘΒΕΔͱ͖
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ
̎ͭͷަব໰୊ ͱ ʹ͓͍ͯ
ͱ͢Δ
΋͠
ͳΒ͹
Ͱ͋Δ
i = 1, 2 ti
≥ fi
(U, d) i
ti
fi
(U, d) U t = (t1
, t2
)
(U, d) f1
(U, d) = f2
(U, d)
d1
= d2
(u1
, u2
) ∈ U (u2
, u1
) ∈ U
(U′

, d′

) (U, d) ui′

= αi
ui
+ βi
, αi
0 (i = 1,2)
fi
(U′

, d′

) = αi
fi
(U, d) + βi
, αi
0 (i = 1,2)
(U, d) (T, d) T ⊂ U
f(U, d) ∈ T f(T, d) = f(U, d)

5. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋश
u2
u1
1
0
(0.75, 0.75)
1
0.75
u2
u1
1
0 1
0.7
0.75
(1, 0.7)
ަব໰୊1:(S1, d) ަব໰୊2:(S2, d)
S1 S2

6. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0
(0.75, 0.75)
1
0.75
u2
u1
1
0 1
0.7
0.75
(1, 0.7)
ަব໰୊1:(S1, d) ަব໰୊2:(S2, d)
S1 S2
ύϨʔτ࠷ద ύϨʔτ࠷ద

7. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0
(0.75, 0.75)
1
0.75
u2
u1
1
0 1
0.7
0.75
(1, 0.7)
ަব໰୊1:(S1, d) ަব໰୊2:(S2, d)
S1 S2
ύϨʔτ࠷ద ύϨʔτ࠷ద
ରশੑ
Nashަবղ

8. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
3

9. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
3
u2
u′

1
1
0 1
0.7 (
3
10
,
7
10)
S′

′

2
ύϨʔτ࠷ద
u′

1
=
3
10
u1
3
10
S′

′

′

2
ަব໰୊2’’:(S′

′

2 ∪ S′

′

′

2 , d)

10. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
3
u2
u′

1
1
0 1
0.7 (
3
10
,
7
10)
S′

′

2
ύϨʔτ࠷ద
u′

1
=
3
10
u1
3
10
S′

′

′

2
ަব໰୊2’’:(S′

′

2 ∪ S′

′

′

2 , d)
ରশੑ

11. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
3
u2
u′

1
1
0 1
0.7 (
3
10
,
7
10)
S′

′

2
ύϨʔτ࠷ద
u′

1
=
3
10
u1
3
10
S′

′

′

2
ަব໰୊2’’:(S′

′

2 ∪ S′

′

′

2 , d)
ରশੑ
‫ݩ‬ͷήʔϜʹ‫·ؚ‬Εͳ͍ͷͰ
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ͕࢖͑ͳ͍
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ
̎ͭͷަব໰୊ ͱ ʹ͓͍ͯ
ͱ͢Δ
΋͠
ͳΒ͹
Ͱ͋Δ
(U, d) (T, d) T ⊂ U
f(U, d) ∈ T f(T, d) = f(U, d)

12. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
7

13. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
7
u2
u′

1
1
0
1
0.7
(
7
10
,
7
10)
S′

′

2
ύϨʔτ࠷ద
u′

1
=
7
10
u1
7
10
S′

′

′

2
ަব໰୊2’’:(S′

′

2 ∪ S′

′

′

2 , d)

14. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
7
u2
u′

1
1
0
1
0.7
(
7
10
,
7
10)
S′

′

2
ύϨʔτ࠷ద
u′

1
=
7
10
u1
7
10
S′

′

′

2
ަব໰୊2’’:(S′

′

2 ∪ S′

′

′

2 , d)
ରশੑ

15. ҎԼͷೋͭͷަব໰୊Λߟ͑Δ͍ͣΕ΋ަবͷෆҰக఺͸
φογϡަবղ͸ʁ
d = (0, 0)
ԋशղ౴
u2
u1
1
0 1
0.7
(1, 0.7)
ަব໰୊2:(S2, d)
S2
ύϨʔτ࠷ద
ަব໰୊2’:(S2 ∪ S′

2, d)
S′

2
10
7
u2
u′

1
1
0
1
0.7
(
7
10
,
7
10)
S′

′

2
ύϨʔτ࠷ద
u′

1
=
7
10
u1
7
10
S′

′

′

2
ަব໰୊2’’:(S′

′

2 ∪ S′

′

′

2 , d)
ରশੑ
Nashަবղ
‫ݩ‬ͷήʔϜʹ‫·ؚ‬ΕΔͷͰ
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ͕࢖͑Δ
ແؔ܎ͳ݁Ռ͔Βͷಠཱੑ
̎ͭͷަব໰୊ ͱ ʹ͓͍ͯ
ͱ͢Δ
΋͠
ͳΒ͹
Ͱ͋Δ
(U, d) (T, d) T ⊂ U
f(U, d) ∈ T f(T, d) = f(U, d)

16. ήʔϜཧ࿦#4*$ԋश
ਓަবήʔϜ
࣍ճɿԋश