20.
G = (N, {Xi}i∈N, {ui}i∈N)
S ⊆ N
XS = Πi∈SXi X{A,B} = {{a1, b1}, {a1, b2}, {a2, b1}, {a2, b2}}
uS = (ui)i∈S u{A,C}({a1, b1, c1}) = (uA({a1, b1, c1}), uC({a1, b1, c1})) = (1,2)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2
N
Xi i
ui i
21.
x ∈ X, y ∈ X T ⊆ N (xT, yNT)
T x y
x = {a1, b1, c1} y = {a2, b2, c2} T = {A, B}
(x{A,B}, y{C}) = {a1, b1, c2}
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2
22.
x ∈ X S ⊆ N
S x yS ∈ XS
uS(yS, xNS) > uS(x)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2
x = {a1, b1, c1}, yS = {a2, b2}
23.
x ∈ X S ⊆ N
x
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2
x = {a1, b1, c1}, yS = {a2, b2}
24.
x ∈ X S ⊆ N
x
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2
x = {a2, b1, c2}, y{A,C} = {a1, c1}
25.
x ∈ X S ⊆ N
x
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2