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where a i denotes the vector of the strategies of all users except user i . If a user
participates, its individual utility is its privacy gain minus its participation cost;
otherwise, it is zero. Note that c i is a relative cost compared to privacy gain.
To take into account the social ties among users, each user i aims to maximize its
social group utility, defined as
f i ( a i , a i )
u i ( a i , a i )
+
s ij u j ( a j , a j ) .
(5.2)
S
i
j N
+
Note that a user does not need to know the individual utilities of its social neighbors
(which may be their private information) to make the decision (as will be shown in
Eq. ( 5.3 )). In Sect. 5.5.3 , we will discuss how social information can be used while
preserving the privacy of users' real identities with each other.
Under the SGUM framework, users' socially-aware decision making for
pseudonym change boils down to a social group utility maximization game. Specifi-
cally, each user i
is a player and its strategy 2 is a i ∈{
, a n )
denote the strategy profile consisting of all users' strategies. The payoff function of a
user is defined as its social group utility function. Given the strategies of other users,
each user i aims to choose the best response strategy that maximizes its social group
utility:
N
0, 1
}
. Let a
=
( a 1 ,
···
maximize
a i
f i ( a i , a i ),
i N .
For the sake of system efficiency, a natural objective is to maximize the social
welfare of the system, which is the total individual utility of all users denoted by
v ( a )
i N
, a n )is social optimal [ 9 ]if
it achieves the maximum social welfare among all profiles, i.e., v ( a )
u i ( a ). A strategy profile a
( a 1 ,
=
···
a .
Although the social optimal profile is the best outcome in terms of system efficiency,
it is often not acceptable by all users. Then, it is desirable to achieve the “best” SNE,
i.e., the SNE that achieves the maximum social welfare among all SNEs. For brevity,
we will refer to this SNE as the best SNE.
Another desirable notion for system efficiency is Pareto-optimality . A strategy
profile a po
v ( a ),
( a p 1 ,
, a p n ) is Pareto-optimal [ 9 ] if there does not exist a Pareto-
=
···
superior profile a
, a n ) such that no user achieves a worse individual
utility while at least one user achieves a better individual utility, i.e.,
( a 1 ,
=
···
u i ( a po
, a po
u i ( a i , a i )
i ),
i
N
i
with at least one strict inequality.
For the SGUM-based PCG, we are interested in answering the following important
questions: Does the game admit a SNE? How can we efficiently find a SNE with
desirable system efficiency?
2 As we focus on pure strategies in this work, we use “strategy” and “action” interchangeably.
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