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Social Group Utility Maximization Game with Applications in Mobile Social Social Group Utility Maximization Game with Applications in Mobile Social

Social Group Utility Maximization Game with Applications in Mobile Social - PowerPoint Presentation

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Social Group Utility Maximization Game with Applications in Mobile Social - PPT Presentation

Networks Xiaowen Gong Xu Chen Junshan Zhang Arizona State University Allerton Conference 2013 Oct 4th 2013 Outline Introduction Social Group Utility Maximization Framework ID: 658801

user social utility game social user game utility sgum control sne network access strategy power group ncg random individual

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Slide1

Social Group Utility Maximization Game with Applications in Mobile Social Networks

Xiaowen Gong, Xu Chen, Junshan ZhangArizona State University

Allerton Conference 2013 Oct. 4th, 2013Slide2

OutlineIntroduction

Social Group Utility Maximization FrameworkRandom Access Control Game under SGUMPower Control Game under SGUMConclusion2Slide3

Non-cooperative Game v.s

. Network Utility Maximization3

Network utility maximization (NUM)

Users are

altruistic

, with the same objective of maximizing the

total

utility of all users

Extensively studied for network resource allocation

Non-cooperative game (NCG)

Each user is selfish, aiming to maximize its individual utilityWidely applied in networking field to model strategic interaction among autonomous network entities

NCG v.s. NUM are two extreme cases: socially oblivious v.s. fully social-ware

Question: What is between these two extremes?Slide4

Mobile Social Network

Mobile social network

Hand-held mobile devices are operated by

human beings

People have

diverse

social relationships and care about their social neighbors at

different

levels (e.g., family, friends, acquaintances)

New framework between NCG and NUM is needed

Social network overlaying mobile networkPhysical domain: physical coupling based on physical relationships

Social domain: social coupling due to social ties among usersSlide5

Social Group Utility Maximization Framework

5

Social graph model

Two users are connected by a

directed

edge if one has social tie towards the other

:

strength

of the social tie from user

to user

with The social tie strength of user to itself is ,  

Social group utility maximization game (SGUM)User are players

: user ’s strategy,

: all users’ strategies except user

’s

:

individual utility

of

user

: social group utility

of user

Each user aims to maximize its

social group utility

 

 Slide6

Social Group Utility Maximization Framework

6

Social-aware Nash equilibrium (SNE)

is a SNE if no

user can

improve its

social

group utility

by unilaterally changing its

strategy 

NCG and NUM are captured under SGUM as special casesIf no social tie exists (i.e., ), SGUM degenerates to NCG as

is a

Nash equilibrium (NE)

if no user can improve its

individual utility

by unilaterally changing its

strategy

If

all

social ties have the

maximum strength (i.e., ), SGUM degenerates to NUM as

is

network optimal (NO) if it maximizes the network utility

 Slide7

Related Work

7

SGUM is different from

cooperative game (CG)

Each user in a CG only cares

individual utility

, although it is achieved through cooperation with other users

A user in a CG can only participate in

one coalition

, while it can be in multiple social groups under SGUM

Little attention paid to the continuum space between NCG and NUMRouting game among altruistic users [Chen et al, 2008] [Hoefer et al, 2009], random access game between two symmetrically altruistic

users [Kesidis et al, 2010]Explore social aspects in networkingExploit social contact pattern

for efficient data forwarding [Costa et al, 2008] [Gao et al, 2009], leverage social trust and reciprocity to improve D2D communication [Chen et al, 2013]

 

 

 

 

 

 

 

 

 

 

c

oalitions in a CG:

{1,2,3}, {4,5}

s

ocial groups under SGUM:

{1,2,3},{3,4,5}Slide8

Random Access Control Model

8

Protocol interference model

Each user

is a link consisting of a transmitter

and a receiver

causes interference

to

if

is in the interference range of

: set of the receivers that causes interference to: set of the transmitters that causes interference to

 

Random access control modelEach user decides access

probability

to

contend

for data transmission

If

multiple

users contend, a collision occurs and no user can grab the transmission opportunity  Slide9

Random Access Control Game under SGUM

9

Random access control game

under SGUM:

: the

successful contention probability

of user

User

’s individual utility

: user

’s

efficiency of utilizing the transmission opportunity (e.g., transmission rate)The log function is widely used to model utility of wireless users 

 

THEOREM 1:

There exists a

unique SNE

in the random access control game under SGUM, and

.

 

Remark: each

user’s SNE

strategy is a

dominant strategySlide10

Random Access Control Game under SGUM

LEMMA 1: The SNE strategy

is decreasing in

.

 

LEMMA 2:

The

network utility

at the SNE is increasing in

, and is optimal when . 

Remark

Each user

decreases

the successful contention probability

of any user

within its interference range if it

increases

its access probability

user

decreases

when the social tie

increases 

Remark

Users’ individual utilities are

equally weighted

in the

n

etwork utility

each user

’s SNE strategy becomes

closer

to the network optimal one when other users’

individual

utilities

weigh more

in user

’s social group utility

 Slide11

Random Access Control Game under SGUM

Remark

As the social

tie strengths

increase

from 0s to

1s

, the SNE

strategy of each player

migrates

from the NE strategy of a NCG to the NO strategy for NUM SGUM spans the continuum space between NCG and NUM 

An example of two-user game with  Slide12

Power Control Model

12

Physical interference model

Each user

is a link consisting of a transmitter

and a receiver

:

t

ransmission channel gain of link

:

interference channel gain from to : noise at  

Power control modelEach user decides transmit power

of

:

signal-to-interference-plus-noise

ratio (SINR)

 

 Slide13

Power Control Game under SGUM

13

Power control game

under SGUM:

User

’s individual utility

: user

’s cost per unit

power consumption

can be a good approximation of the channel capacity  

THEOREM 2: The power control game under SGUM is a supermodular game

, and hence it has

at least one SNE.

Remark

The game is

supermodular

if

Since the game is

supermodular

, each user

can update its strategy

with

best response from , such that it will monotonically converge to the SNE

 Slide14

Power Control Game under SGUM

14

We focus on

two-user

power control game under SGUM

Provide useful insight into the

impact of social ties

The game with more users is difficult for analysis

THEOREM 3:

There exists a

unique SNE in the two-user power control game under SGUM, and

, , where

,

,

,

.

 

Remark: each

user’s SNE

strategy is a

dominant strategy

LEMMA 3:

The SNE strategy

is

decreasing

in

and

is

decreasing

in

.

 

Remark

Each user

decreases

the SINR

of another user

if it

increases

its transmit power

user

decreases

when the social tie

increases

 Slide15

Power Control Game under SGUM

LEMMA 4: The network utility at the SNE is

increasing in

and

, and is

optimal

when

.

 

Remark

Similar to the random access control game under SGUM, the network utility improves when the other user’s individual utility weighs more in a user’s social group utility

SGUM spans the continuum space between NCG and NUM

An example of two-user game with

 Slide16

Conclusion

Contribution

Developed

social group utility maximization (SGUM)

framework that bridges the gap between

non-cooperative game

and

network utility maximization

, two traditionally disjoint paradigms

Showed that there exists a unique social-aware Nash equilirium (SNE) in the random access control game under SGUM, and investigated the

impact of social ties on the SNE strategy and network utilityShowed that the power control game under SGUM is a supermodular game and hence has at least one SNE, and investigated the impact of social ties for the two-user case

Future workSGUM provides rich modeling flexibility by spanning the continuum space between NCG and NUMStudy SGUM game for more applications (e.g., spectrum access) and investigate the impact of social ties on different performance metrics (e.g., fairness)Slide17