Information Technology Reference
In-Depth Information
Fig. 3.3
Impact of number of
users
1.3
NCG
SGUM−ER
SGUM−real
NUM
1.2
1.1
1
10
11
12
13
14
15
16
17
18
19
20
Number of users
(1
1
+
c
i
+
+
c
i
)
2
−
4
c
i
≥
≥
1,
2
c
i
∂V
(
q
)
∂q
i
[
q
SO
i
we have
<
0 for
q
i
∈
, 1], and thus
V
(
q
) is decreasing in
q
i
when
[
q
SO
i
, 1]. Using Corollary
3.1
,
q
SNE
i
∈
I
i
q
i
∈
is decreasing in
s
ij
,
∀
j
,
∀
i
∈
N
, and
hence
V
(
q
SNE
) is increasing in
s
ij
,
∀
j
∈
I
i
,
∀
i
∈
N
.
Remark 3.2
. Intuitively, since the social welfare is equal to users' individual utilities
summed up with the same weight 1, a user's SNE strategy is closer to the social
optimal strategy when other users weigh more in that user's social group utility
(i.e., the social tie levels to them increase), and the social welfare increases. As
social tie levels increase, a user's SNE strategy migrates from its NE strategy for a
standard NCG to its social optimal strategy for NUM (as illustrated in Fig.
3.2
). This
demonstrates that the SGUM game framework spans the continuum between these
traditionally disjoint paradigms.
3.2.3
Numerical Results
We consider
N
users each of which is a link consisting of a transmitter and a re-
ceiver. Each transmitter or receiver is randomly located in a square area with side
length 500 m. Under the protocol interference model, we assume that a link causes
interference to another link if the former link's transmitter is within 100 m of the
latter link's receiver. We simulate the social graph based on both the Erdos-Renyi
(ER) model with link probability 0
.
5 and the real data trace of the friendship network
Brightkite. We assume that the strength of a social tie is 1 if the social tie exists.
To illustrate the system efficiency of the SGUM solution, we compare it with
the NCG solution where each user aims to maximize its individual utility, and the
NUM solution where the total individual utility of all users is maximized. Figure
3.3
depicts the social welfare of the SNE for SGUM and the social optimal solution for
NUM normalized with respect to the NE for NCG, as the number of users increases.
