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On the Windfall of Friendship: Inoculation Strategies on Social Networks

Explore the dynamics of friendship on social networks through inoculation strategies. Investigate how the Windfall of Friendship impacts virus propagation and equilibrium in social network games. This study introduces a new model that considers the wellbeing of friends in decision-making processes, offering insights into the cost-benefit analysis of protection mechanisms in network interactions. Discover the implications of incorporating friendship factors into strategic choices and equilibrium outcomes in social network scenarios.

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On the Windfall of Friendship: Inoculation Strategies on Social Networks

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  1. On the Windfall of Friendship: Inoculation Strategies on Social Networks Dominic Meier Yvonne Anne Oswald Stefan Schmid Roger Wattenhofer

  2. Yvonne Anne Oswald @ EC 2008 History of behavioural network models Once upon a time... ... every node follows protocol • malicious nodes • selfish/rational nodes (game theory meets computer science) now still no explanation for behaviour of real networks

  3. Yvonne Anne Oswald @ EC 2008 New model: care about your friends’ wellbeing “Traditional“ game theory: player pi selects strategy ai=> strategy profile a actual cost for player pi : costa(i,a) “Friendly“ game theory: consider cost of friends : F 2 [0,1] Friendship Factor perceived cost cp(i,a) = ca(i,a) + F ¢ ca(j,a) neighbour pj • new equilibria (FNE) cost(aworstNE) cost(aworstFNE) ____________ Windfall of Friendship WoF(F) =

  4. Case study: virus inoculation game [Aspnes et al., SODA 2005] social networks everywhere: facebook, co-authors, email .... => many connections => fast virus distribution Yvonne Anne Oswald @ EC 2008

  5. Virus inoculation game [Aspnes et al., SODA 2005] social networks everywhere: facebook, co-authors, email .... => many connections => fast virus distribution Yvonne Anne Oswald @ EC 2008

  6. Virus inoculation game [Aspnes et al., SODA 2005] social networks everywhere: facebook, co-authors, email .... => many connections => fast virus distribution • Solution: • invest in protection • but • $$$ • if all neighbours are protected no need for get protected as well.. invest if expected damage > cost Yvonne Anne Oswald @ EC 2008

  7. Virus Inoculation Game - Example Yvonne Anne Oswald @ EC 2008

  8. Virus Inoculation Game - Example Yvonne Anne Oswald @ EC 2008

  9. Virus Inoculation Game – Example Yvonne Anne Oswald @ EC 2008

  10. Virus Inoculation Game - Example Yvonne Anne Oswald @ EC 2008

  11. Yvonne Anne Oswald @ EC 2008 Virus Inoculation Game - Example

  12. Virus Inoculation Game - Example Yvonne Anne Oswald @ EC 2008

  13. Yvonne Anne Oswald @ EC 2008 Model [Aspnes et al., SODA 2005] • network of n devices • owner of node decides whether to protect it or not • inoculation cost: C • infection cost: L • virus infection at 1 arbitrary initial node • virus propagation over paths of insecure devices

  14. Actual cost [Aspnes et al., SODA 2005] strategies of pi ai = 0 : device is not protected ai = 1 : device is protected C if ai = 1 ca(i,a) = L¢ ki/n if ai = 0 ki = size of attack component of pi actual cost: (per node) social cost (network) cost(a) = pi ca(i,a) Yvonne Anne Oswald @ EC 2008

  15. Previous results • [Aspnes et al., SODA 2005] • pure equilibria always exist • attack components of size Cn/L • PoA (price of anarchy) linear in n • [Moscibroda et al., PODC 2006] • Malicious nodes: lie about their strategies Yvonne Anne Oswald @ EC 2008

  16. Introducing friendship F 2 [0,1] Friendship Factor cp(i,a) = ca(i,a) + F¢pj neighbour ca(j,a) perceived cost: (per node) cost(aworstNE) cost(aworstFNE) ____________ Windfall of Friendship WoF(F) = cost(a) = pi ca(i,a) Yvonne Anne Oswald @ EC 2008

  17. Results PoA ≤ n [Aspnes et al., SODA’05] General graphs • attack components size depends on topology • WoF(F) ≥ 1 • WoF(F) ≤ PoA • WoF(F) is not monotonically increasing in F • computing worst/best FNE is NP-complete Example Yvonne Anne Oswald @ EC 2008

  18. WoF(F) is NOT monotonically increasing in F social optimum total cost = 4.69 n = 13 C = 1 L = 4 Yvonne Anne Oswald @ EC 2008

  19. WoF(F) is NOT monotonically increasing in F selfish setting total cost = 12.76 n = 13 C = 1 L = 4 PoA = 2.73 Yvonne Anne Oswald @ EC 2008

  20. WoF(F) is NOT monotonically increasing in F friendly setting total cost = 12.23 n = 13 C = 1 L = 4 F = 0.9 WoF(0.9) = 1.04 Yvonne Anne Oswald @ EC 2008

  21. WoF(F) is NOT monotonically increasing in F friendly setting total cost = 4.69 n = 13 C = 1 L = 4 F = 0.1 WoF(0.1) = 2.73 Yvonne Anne Oswald @ EC 2008

  22. Results General graphs • WoF(F) ≥ 1 • WoF(F) ≤ PoA • WoF(F) is not monotonically increasing in F • computing worst/best FNE is NP-complete Reduction from vertex cover and independent dominating set Yvonne Anne Oswald @ EC 2008

  23. Results Special graphs • a FNE always exists, fast convergence • WoF(F) ≤ 4/3 (tight) complete graph • a FNE always exists, fast convergence • sometimes the best FNE is the only FNE • 1 FNE => WoF(F) can reach n more than 1 FNE => WoF(F) = O(1) star graph Yvonne Anne Oswald @ EC 2008

  24. Results Special graphs • a FNE always exists, fast convergence • WoF(F) ≤ 4/3 (tight) complete graph • a FNE always exists, fast convergence • sometimes the best FNE is the only FNE • 1 FNE => WoF(F) linear in n more than 1 FNE => WoF(F) = O(1) star graph Yvonne Anne Oswald @ EC 2008

  25. Future directions... • analyze more complex graphs and real social networks • variations of virus game - more than 1 virus - more strategies - other propagation models • analyze other games on networks • generalize model - include k-hop neigbours - weighted graph: Fi,j - ... Yvonne Anne Oswald @ EC 2008

  26. Moral of the story There is nothing bad in being social, even for computer scientists and economists ... Yvonne Anne Oswald @ EC 2008

  27. The End! Thank you! Questions? Comments? Yvonne Anne Oswald @ EC 2008

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