The document describes a game theory model involving two players and their strategies. It defines the players, their possible actions, and the payoffs they receive based on the combination of strategies chosen. It also analyzes the strategies in terms of game theory solution concepts like Nash equilibria.

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