The document describes a model consisting of a set of nodes N and sets of variables and utilities assigned to each node. Tuples are formed from combinations of the variable values. The utility of a given tuple for a set of nodes S is defined as the sum of the utilities of the individual nodes in S. A deviation is possible from a current tuple x to an alternate y if the utility of y for a subset of nodes S is greater than the utility of x for S. This model is used to represent situations where subsets of agents have incentive to deviate from the current state to improve their payoffs.

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2. 1.
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3. 1.
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(b)
2.
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(b)
(c)

5.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

6.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

7.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

8.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

9.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

10.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

11.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

12.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

13.
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

14.
(a1, b1, c1) (a2, b2, c1) (a2, b1, c2)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

15.
(a1, b1, c1) (a2, b2, c1) (a2, b1, c2)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

16.
(a1, b1, c1) (a2, b2, c1) (a2, b1, c2)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

17.
(a1, b1, c1)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

18.
(a1, b1, c1)
A BA B
c1
a1
a2
a1
a2
b1 b2 b1 b2
c2

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

28. See you next time