https://youtu.be/TZa2G5RC_As

1. ήʔϜཧ࿦#4*$ԋश
σʔτήʔϜͱલ޲͖‫ؼ‬ೲ๏

2. σʔτήʔϜͰͷφογϡ‫ߧۉ‬
σʔτήʔϜͰͷ෦෼ήʔϜ‫׬‬શ‫ߧۉ‬
ऑࢧ഑ͷഉআʹΑϦ࢒Δઓུ

3. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
ϓϨΠϠʔ͕ʮIPNF Ոʹ͍Δ͜ͱΛબ୒
ʯ͔ʮPVU ͓ग़͔͚
ʯΛબͿ
ͦͷ‫
ޙ‬#BUUMFPGUIFTFYFT உঁͷ૪͍
ΛϓϨΠ͢Δ
σʔτήʔϜʹ͓͚Δ७ઓུφογϡ‫ߧۉ‬Λ‫ٻ‬ΊΑ
σʔτήʔϜʹ͓͚Δ෦෼ήʔϜ‫׬‬શ‫ߧۉ‬Λ‫ٻ‬ΊΑ
ऑࢧ഑͞ΕΔઓུΛஞ࣍আ‫࢒ͯ͠ڈ‬ΔઓུΛ‫ٻ‬ΊΑ
σʔτήʔϜ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
৘ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)

4. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
σʔτήʔϜʹ͓͚Δ७ઓུφογϡ‫ߧۉ‬Λ‫ٻ‬ΊΑ
ϓϨΠϠʔͷ७ઓུ͸
ϓϨΠϠʔͷ७ઓུ͸
Ҏ্ΑΓ
φογϡ‫ߧۉ‬͸
home − movie home − shopping out − movie out − shopping
movie, shopping
(home − movie, movie) (home − shopping, movie) (out − shopping, shopping)
σʔτήʔϜ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
৘ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
1ʘ2
home − movie
home − shopping
out − movie
out − shopping
movie shopping

5. ෦෼ήʔϜ‫׬‬શ‫ߧۉ‬
ఆٛ ෦෼ήʔϜ‫׬‬શ‫
ߧۉ‬
ల։‫ܗ‬ήʔϜ ʹ͓͍ͯ
ߦಈઓུ ͕෦෼ήʔϜ‫׬‬શ‫͋Ͱߧۉ‬Δͱ͸
͢΂ͯͷ෦෼ήʔϜʹରͯ͠
͕φογϡ‫ߧۉ‬Λಋ͘͜ͱͰ͋Δ
#4*$ୈճΑΓൈਮ
Γ = (K, p, P, U, h) b* = (b*1
, ⋯, b*n
)
b*
u1
1
u2
1
P1
P2
P2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(0, 0)
(10, 5)
(5, 10)
(0, 0)
u2
2
ɿ෦෼ήʔϜ
Γ′

ɿ෦෼ήʔϜ
Γ′

′

ϓϨΠϠʔ͕෦෼ήʔϜ Ͱ
࠷దͳߦಈΛͱ͍ͬͯͳ͍
Γ′

′

u1
1
u2
1
P1
P2
P2
a1
1
a1
2
a2
1
a2
2
a2
3
a2
4
(0, 0)
(10, 5)
(5, 10)
(0, 0)
u2
2
ɿ෦෼ήʔϜ
Γ′

ɿ෦෼ήʔϜ
Γ′

′

ɿશମͷήʔϜ ෦෼ήʔϜͱΈͳ͢
Γ

6. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
σʔτήʔϜʹ͓͚Δ෦෼ήʔϜ‫׬‬શ‫ߧۉ‬Λ‫ٻ‬ΊΑ
෦෼ήʔϜʹ͓͚Δφογϡ‫ߧۉ‬Λߟ͑Δͱ
ͱ Ͱ͋Δ
ɾ෦෼ήʔϜͰ ͕औΒΕΔͱ͢Ε͹ϓϨΠϠʔ͸ ΛબͿͷ͕࠷ద
ɾ෦෼ήʔϜͰ ͕औΒΕΔͱ͢Ε͹
ϓϨΠϠʔ͸ ΛબͿͷ͕࠷ద
Ώ͑ʹ
෦෼ήʔϜ‫׬‬શ‫ߧۉ‬͸
(movie, movie) (shopping, shopping)
(movie, movie) home
(shopping, shopping)
out
(home − movie, movie) (out − shopping, shopping)
σʔτήʔϜ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
৘ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
1ʘ2
movie
shopping
movie shopping
෦෼ήʔϜ
෦෼ήʔϜ
P1
(2, 0)
home out
(1, 3)
P1
(2, 0)
home out
(3, 1)

7. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
ऑࢧ഑͞ΕΔઓུΛஞ࣍আ‫࢒ͯ͠ڈ‬ΔઓུΛ‫ٻ‬ΊΑ
ϓϨΠϠʔͷ ͸
΍ ʹऑࢧ഑͞ΕΔ
out − movie
home − movie home − shopping
σʔτήʔϜ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
৘ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
ϓϨΠϠʔ ͷ̎ͭͷઓུ ʹ͍ͭͯ
Λຬͨ͢ͱ͖ ͸ Λऑࢧ഑͢Δͱ͍͏
͋Δઓུ ͕ Λऑࢧ഑͢Δͱ͖ ͸ऑࢧ഑͞ΕΔͱ͍͏
i si
, s′

i
∈ Si
fi
(si
, s−i
) ≥ fi
(s′

i
, s−i
), ∀s−i
∈ S−i
fi
(si
, s′

−i
) fi
(s′

i
, s′

−i
), ∃s′

−i
∈ S−i
si
s′

i
si
s′

i
s′

i
1ʘ2
home − movie
home − shopping
out − movie
out − shopping
movie shopping

8. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
ऑࢧ഑͞ΕΔઓུΛஞ࣍আ‫࢒ͯ͠ڈ‬ΔઓུΛ‫ٻ‬ΊΑ
ϓϨΠϠʔͷ ͸
΍ ʹऑࢧ഑͞ΕΔ
ϓϨΠϠʔͷ ͸ ʹऑࢧ഑͞ΕΔ
out − movie
home − movie home − shopping
movie shopping
σʔτήʔϜ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
৘ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
ϓϨΠϠʔ ͷ̎ͭͷઓུ ʹ͍ͭͯ
Λຬͨ͢ͱ͖ ͸ Λऑࢧ഑͢Δͱ͍͏
͋Δઓུ ͕ Λऑࢧ഑͢Δͱ͖ ͸ऑࢧ഑͞ΕΔͱ͍͏
i si
, s′

i
∈ Si
fi
(si
, s−i
) ≥ fi
(s′

i
, s−i
), ∀s−i
∈ S−i
fi
(si
, s′

−i
) fi
(s′

i
, s′

−i
), ∃s′

−i
∈ S−i
si
s′

i
si
s′

i
s′

i
1ʘ2
home − movie
home − shopping
out − shopping
movie shopping

9. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
ऑࢧ഑͞ΕΔઓུΛஞ࣍আ‫࢒ͯ͠ڈ‬ΔઓུΛ‫ٻ‬ΊΑ
ϓϨΠϠʔͷ ͸
΍ ʹऑࢧ഑͞ΕΔ
ϓϨΠϠʔͷ ͸ ʹऑࢧ഑͞ΕΔ
ϓϨΠϠʔͷ ͸
ʹऑࢧ഑͞ΕΔ
Ҏ্ΑΓ
࢒Δઓུ͸ϓϨΠϠʔͷ
ϓϨΠϠʔͷ
out − movie
home − movie home − shopping
movie shopping
home − movie home − shopping
out − shopping
out − shopping shopping
σʔτήʔϜ
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
৘ใू߹
ϓϨΠϠʔ
P1
ϓϨΠϠʔ
P2
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)
ϓϨΠϠʔ ͷ̎ͭͷઓུ ʹ͍ͭͯ
Λຬͨ͢ͱ͖ ͸ Λऑࢧ഑͢Δͱ͍͏
͋Δઓུ ͕ Λऑࢧ഑͢Δͱ͖ ͸ऑࢧ഑͞ΕΔͱ͍͏
i si
, s′

i
∈ Si
fi
(si
, s−i
) ≥ fi
(s′

i
, s−i
), ∀s−i
∈ S−i
fi
(si
, s′

−i
) fi
(s′

i
, s′

−i
), ∃s′

−i
∈ S−i
si
s′

i
si
s′

i
s′

i
1ʘ2
home − movie
home − shopping
out − shopping
shopping

10. ҎԼͷల։‫ܗ‬ήʔϜͰද‫͞ݱ‬ΕΔήʔϜΛσʔτήʔϜͱ‫͢ʹͱ͜Ϳݺ‬Δ
७ઓུφογϡ‫ߧۉ‬
෦෼ήʔϜ‫׬‬શ‫ߧۉ‬
ऑࢧ഑͞ΕΔઓུͷআ‫࢒Ͱڈ‬Δઓུͷ૊
ϓϨΠϠʔ͕ҙࢥܾఆ͢Δͱ͍͏͜ͱ͸ϓϨΠϠʔ͕ʮPVUʯΛબΜͩ৔߹Ͱ͋Δ
·ͨ
ϓϨΠϠʔ͸ʮIPNFʯΛબ΂͹࣮֬ʹͷརಘΛಘΒΕΔΘ͚Ͱ
ͦΕʹ΋ؔΘΒͣʮPVUʯΛબΜͰ͖͍ͯΔ
ϓϨΠϠʔͱͯ͠͸
ϓϨΠϠʔ͕߹ཧతͰ͋Δͱߟ͑ΔͷͰ͋Ε͹ʮPVUʯΛબΜͩ͜ͱ͔Β
ϓϨΠϠʔ͸ʮTIPQQJOHʯΛબͿͱ༧૝͢΂͖Ͱ͋Δ
͜ͷ༧૝ͷ΋ͱͰ͸ϓϨΠϠʔ͸ʮTIPQQJOHʯΛબͿͷ͕࠷దʹͳΔ
ະདྷͷߦಈ͔Β༧૝͢ΔͷΛ‫ޙ‬Ζ޲͖‫ؼ‬ೲ๏ͱ‫Ϳݺ‬ͷʹର͠
ա‫ڈ‬ͷߦಈ͔Β༧૝͢ΔͷͰલ޲͖‫ؼ‬ೲ๏ͱ‫ݺ‬͹ΕΔ
(home − movie, movie) (home − shopping, movie) (out − shopping, shopping)
(home − movie, movie) (out − shopping, shopping)
(out − shopping, shopping)
લ޲͖‫ؼ‬ೲ๏
P1
P2
P1
(2, 0)
(0, 0)
home
σʔτήʔϜ
P2
(1, 3)
out
movie
m
shopping
s
movie shopping
(3, 1)
(0, 0)

11. ήʔϜཧ࿦#4*$ԋश
σʔτήʔϜͱલ޲͖‫ؼ‬ೲ๏
࣍ճɿԋश