1. Social Group Utility Maximization Game with Applications in Mobile Social Networks Xiaowen Gong, Xu Chen, Junshan Zhang Arizona State University Allerton Conference 2013 Oct. 4th, 2013

2. Outline Introduction Social Group Utility Maximization Framework Random Access Control Game under SGUM Power Control Game under SGUM Conclusion 2

3. Non-cooperative Game v.s. Network Utility Maximization 3 Network utility maximization (NUM) o Users are altruistic, with the same objective of maximizing the total utility of all users o Extensively studied for network resource allocation Non-cooperative game (NCG) o Each user is selfish, aiming to maximize its individual utility o Widely 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?

4. Mobile Social Network Mobile social network o Hand-held mobile devices are operated by human beings o People have diverse social relationships and care about their social neighbors at different levels (e.g., family, friends, acquaintances) o New framework between NCG and NUM is needed Social network overlaying mobile network o Physical domain: physical coupling based on physical relationships o Social domain: social coupling due to social ties among users

5. Social Group Utility Maximization Framework 5

6. 6

7. Related Work 7 SGUM is different from cooperative game (CG) o Each user in a CG only cares individual utility, although it is achieved through cooperation with other users o 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 NUM o Routing 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 networking o Exploit 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] coalitions in a CG: {1,2,3}, {4,5} social groups under SGUM: {1,2,3},{3,4,5}

8. Random Access Control Model 8

9. Random Access Control Game under SGUM 9 Remark: each user’s SNE strategy is a dominant strategy

10. Random Access Control Game under SGUM

12. Power Control Model 12

13. Power Control Game under SGUM 13 THEOREM 2: The power control game under SGUM is a supermodular game, and hence it has at least one SNE.

14. Power Control Game under SGUM 14 We focus on two-user power control game under SGUM o Provide useful insight into the impact of social ties o The game with more users is difficult for analysis Remark: each user’s SNE strategy is a dominant strategy

15. Power Control Game under SGUM Remark o 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 o SGUM spans the continuum space between NCG and NUM

16. Conclusion Contribution o Developed social group utility maximization (SGUM) framework that bridges the gap between non-cooperative game and network utility maximization, two traditionally disjoint paradigms o 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 utility o Showed 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 work o SGUM provides rich modeling flexibility by spanning the continuum space between NCG and NUM o Study SGUM game for more applications (e.g., spectrum access) and investigate the impact of social ties on different performance metrics (e.g., fairness)