Xu Chen Xiaowen Gong Lei Yang Junshan Zhang

1. A Social Group Utility Maximization Framework with Applications in Database Assisted Spectrum Access Xu Chen Xiaowen Gong Lei Yang Junshan Zhang School of Electrical, Energy, and Computer Engineering Arizona State University

2. Outline • Introduction • Social Group Utility Maximization Framework • Database-assisted Spectrum Access under SGUM • Conclusion and Future Work

3. When Mobile Network Meets Social Network • Mobile networks are ubiquitous • Mobile phone shipments is projected to reach 1.9 billion in 2014 (about 7 times that of desktop and laptop combined), mobile data traffic more than doubled in 2013 • Advanced wireless technology (e.g., MIMO, OFDM), powerful wireless devices (e.g., smartphone, wearable smart devices) • Social networks shape people’s behavior • Social relationships have pervasive impact (e.g., social media, social recommendation) • Online social networks users in 2013 crossed 1.7 billion (about one quarter of world’s population)

4. Social Dimension on Mobile Networking • Key observations on mobile network • Mobile devices are personal communication devices carried and operated by human beings • People have diverse social ties and care about their social neighbors at different levels (e.g., family, friend, acquaintance)

5. Virtual Social Network Underlays Physical Communication Network Physical Domain 2 5 Physical Coupling 1 4 3 Social Domain 2 5 4 Social Coupling 1 3 • Question: Can we exploit social ties among mobile users to improve the interactions of their mobile devices in communication networks? How can we leverage it cleverly? • Physical-social coupling among mobile devices • Physical domain: physical coupling subject to physical relationship • Social domain: social coupling due to social ties among users

6. From Non-cooperative Game to Network Utility Maximization • Non-cooperative game (NCG) • Each user is selfish, aiming to maximize its individual utility • Widely used to study strategic interaction among autonomous users Altruistic Selfish Users’ Social Awareness • Network utility maximization (NUM) • Users are altruistic, aiming to maximize social welfare • Extensively studied for network resource allocation Non-Cooperative Game Network Utility Maximization Answer: Social group utility maximization (SGUM): A new paradigm on mobile social networking • NCG and NUM are two extreme cases: selfish (social-oblivious) or altruistic (fully social-aware) Question: What is between these two extremes?

7. Outline • Introduction • Social Group Utility Maximization Framework • Database-assisted Spectrum Access under SGUM • Conclusion and Future Work

8. Physical Graph Model • A set of mobile users • User-specific feasible strategy set (e.g., channel selection, power level selection) • Physical graph • Two users are connected by a physical edge if they have physical coupling • Capture the physical relationships among users (e.g., interference) • the set of users having physical coupling with user • Individual utility • User’s payoff under strategy profile (e.g., SINR, data rate) • Depend on the physical graph (e.g., interference graph)

9. Social Graph Model • Social graph • Two users are connected by a social edge if they have a social tie • Capture the social coupling among users (i.e., kinship, friendship) • : the set of users user has social ties with • : social tie strength from user to user • From individual utility to social group utility weighted sum of individual utilities of user ’s social neighbors user ’s individual utility

10. Social Group Utility Maximization Game • Distributed decision making among users • Each user aims to maximize its social group utility • Social group utility maximization (SGUM) game •  player set •  strategy space of player •  payoff function of player • Social-aware Nash equilibrium (SNE) • is a SNE if no user can improve its social group utility by unilaterally changing its strategy

11. Social Group Utility Maximization • SGUM provides rich modeling flexibility • If no social tie exists (i.e., ), SGUM degenerates to NCG as • If all social ties have the maximum strength (i.e., ), SGUM becomes NUM as • Span the continuum space between NCG and NUM Social group utility maximization (SGUM)framework captures diverse social ties of mobile users and diverse physical relationships of mobile devices;it spans the continuum space between non-cooperative game and network utility maximization. 1 2 Selfish Altruistic 3 4 Social-aware SGUM NUM NCG SGUM 1 2 1 2 selfish altruistic 3 4 3 4 NCG NUM

12. Related Work • Explore social aspectfor wireless networks • Exploit social contact pattern for efficient data forwarding [Gao et al, 2009]; leverage social trust and reciprocity to improve D2D communication [Chen et al, 2013] • Routing game among altruistic users [Chen et al, 2008] [Hoefer et al, 2009], random access game between two symmetricallysocial-awareusers [Kesidis2010] • SGUM game is notcoalition game (CG) • Each user in a CG only cares about itsown utility (though it is achieved through cooperation with others) • A user in a CG can only join one coalition, while it can be in multiple social groups in a SGUM game coalitions in a CG: {1,2,3}, {4,5} social groups under SGUM: {1,2,3},{3,4,5}

13. Outline • Introduction • Social Group Utility Maximization Framework • Database Assisted Spectrum Access under SGUM • Conclusion and Future Work

14. Database Assisted Spectrum Access • FCC recent ruling on TV spectrum utilization • White-space users determine vacant channels via geo-location database • Obviate the need of spectrum sensing for individual users • Challenges for achieving efficient shared spectrum access • Access the same vacant channel  cause severe interference • Effective cooperationincentivesfor spectrum access is needed

15. SGUM-based Spectrum Access Game • A set of white-space users • Each user selects a vacant channel from a specific set • Physical graph • Two users are connected by a physical edge  they can cause interference to each other • Individual utility • Each user aims to minimize its total interference plus noise • Social group utility

16. SGUM-based Spectrum Access Game THEOREM: Social group utility maximization game for database assisted spectrum access is a potential game and always admits a SNE. • Potential game: if the game has a potential function such that • Property: any strategy that locallymaximizes the potential function is a Nash equilibrium • Potential function of the SGUM game Due to physical coupling Due to social coupling

17. Distributed Spectrum Access Algorithm • How to achievea SNE with a good social welfare? • The strategy that (globally)maximizes the potential function is appealing, but it is a combinatorial problem that is hard to solve in general • Distributed algorithm is desirable • Distributed spectrum access algorithm • Inspired by adaptive CSMA for NUM [Jiang et al, 2010] • Key idea: coordinate users’ asynchronous channel selection updates to form a Markov chain, and drive it to the stationary distribution, which asymptotically maximizesthepotential function

18. Distributed Spectrum Access Algorithm • Each user repeats following steps in parallel: • Compute the social group utility on the current channel based on the individual utilities reported by social neighbors • Set a randomtimer following the exponential distribution • Count down until the timer expires

19. Distributed Spectrum Access Algorithm • Each user repeats following operations in parallel: • Whenthe timer expires, choose a newchannel randomly • Compute the social group utility on the new channel • Decision update: stay in the new channel with probability ; or move back to the original channel with probability

20. Distributed Spectrum Access Algorithm • The distributed algorithm induces a Markov chain • System state: the channel selection profile of all users • Each state transition involves one user: due to the property of exponential distribution for channel update countdown • Two-user Markov chain example: Markov Chain For Dynamic Channel Selection (1,2) (1,3) Vacant Channel Set {2, 3} {1, 2} Channel of User B: Channel of User A: Channel 1 Channel 2 (2,2) (2,3)

21. Distributed Spectrum Access Algorithm • The distributed algorithm induces a Markov chain • System state: the channel selection profile of all users • Each state transition involves one user: due to the property of exponential distribution for channel update count-down • Two-user Markov chain example: Markov Chain For Dynamic Channel Selection (1,2) (1,3) Vacant Channel Set User B Updates Channel Selection {2, 3} {1, 2} Channel of User B: Channel of User A: Channel 1 Channel 3 (2,2) (2,3)

22. Distributed Spectrum Access Algorithm • The distributed algorithm induces a Markov chain • System state: the channel selection profile of all users • Each state transition involves one user: due to the property of exponential distribution for channel update count-down • Two-user Markov chain example: Markov Chain For Dynamic Channel Selection (1,2) (1,3) Vacant Channel Set User A Updates Channel Selection {2, 3} {1, 2} Channel of User B: Channel of User A: Channel 2 Channel 3 (2,2) (2,3)

23. Distributed Spectrum Access Algorithm • The distributed algorithm induces a Markov chain • System state: the channel selection profile of all users • Each state transition involves one user: due to the property of exponential distribution for channel update count-down • Two-user Markov chain example: Markov Chain For Dynamic Channel Selection (1,2) (1,3) Vacant Channel Set User B Updates Channel Selection {2, 3} {1, 2} Channel of User B: Channel of User A: Channel 2 Channel 2 (2,2) (2,3)

24. Distributed Spectrum Access Algorithm • The distributed algorithm induces a Markov chain • System state: the channel selection profile of all users • Each state transition involves one user: due to the property of exponential distribution for channel update count-down • Two-user Markov chain example: diagram of all feasible state transitions Markov Chain For Dynamic Channel Selection (1,2) (1,3) Vacant Channel Set {2, 3} {1, 2} User A User B (2,2) (2,3)

25. Distributed Spectrum Access Algorithm • The distributed algorithm induces a Markov chain • System state: the channel selection profile of all users • Each state transition involves one user: due to the property of exponential distribution for channel update count-down • Two-user Markov chain example THEOREM: The distributed spectrum access algorithm induces a time-reversible Markov chain with the unique stationary distribution given as • As , the SNE can be achieved • For finite , the gap from is bounded by , where is the number of states in Markov chain

26. Performance Gap • Performance gap from the social optimal strategy by NUM • maximum social welfare: where THEOREM: The performance gap of the SNE found by the distributed spectrum access algorithm is at most • decreases as the social tie strength increases • when all users are altruistic, i.e.,

27. Numerical Results • N=100 users randomly scatter over a square area • Physical graph is generated based on users’ distances

28. Numerical Results • Social graph is generated by Erdos-Renyi random graph model • There exists a social link between two users with probability • Performance improves as the social link probability increases • The SNE for the SGUM game migrates monotonically from the NE for NCG to the social optimal strategy for NUM

29. Outline • Introduction • Social Group Utility Maximization Framework • Database-assisted Spectrum Access under SGUM • Conclusion and Future Work

30. Conclusion • Contribution • Developed the social group utility maximization (SGUM) framework, which captures diverse social ties of mobile users and diverse physical relationships of mobile devices, and spans the continuum between non-cooperative game and network utility maximization • Studied SGUM game for database assisted spectrum access, showed that it is a potential game, developed a CSMA-like distributed algorithm to achieve a social-aware Nash equilibrium, and quantified the impact of social ties

31. Future Work • Study a variety of applications under the SGUM framework • E.g, power control, random access control • Extend the SGUM framework to “negative” social ties • Social tie can be “negative” (i.e., ) such that a user intends to damage another’s welfare (e.g., against opponent or enemy) • Zero-sum game (ZSG) • Users aim to minimize others’ welfare • Employed for security applications • If total strength of social ties to each user is zero (i.e., ), SGUM degenerates to ZSG as (e.g, , )

32. Future Work Selfish Malicious Altruistic Negative Social Tie Positive Social Tie ZSG SGUM SGUM NUM NCG 1 2 3 4 SGUM 1 2 1 2 1 2 selfish selfish malicious altruistic 3 4 3 4 3 4 NCG NUM ZSG

33. Thank You!