Social Group Utility Maximization Framework - Social Group Utility Maximization - page 8

Fig. 2.2 The social group
utility maximization (SGUM)
game captures
non-cooperative game (NCG)
and network utility
maximization (NUM) as
special cases

It is worth noting that under different social graphs, the proposed SGUM game
formulation can provide rich flexibility for modeling network optimization problems
(as illustrated in Fig. 2.2 ). When the social graph consists of isolated nodes with
s nm =

(i.e., all users are socially-oblivious), the SGUM game
degenerates to a standard non-cooperative game. When the social graph is fully
meshed with edge weight s nm =

0 for any n , m ∈ N

(i.e., all users are fully altruistic),
the SGUM game becomes a network utility maximization problem, which aims
to maximize the system-wide utility. The SGUM framework can be applied with
general social graphs and thus can bridge the gap between non-cooperative game
and network utility maximization—two traditionally disjoint paradigms for network
optimization (as illustrated in Fig. 2.3 ). These two paradigms are captured under the
SGUM framework as two special cases where no social tie exists among users, and
all users are connected by strongest social ties, respectively.
We emphasize that the SGUM game is quite different from a coalitional game [ 1 ],
since each user in the latter aims to maximize its individual benefit (although it
is achieved by cooperating with other users). Furthermore, while each user in a
coalitional game can only participate in one coalition, a user in the SGUM game can
be in multiple social groups of different users.

1 for any n , m ∈ N

Fig. 2.3 The social group utility maximization (SGUM) framework spans the continuum between
non-cooperative game (NCG) and network utility maximization (NUM)