on the windfall of friendship: inoculation strategies on social networks
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On the Windfall of Friendship: Inoculation Strategies on Social Networks. Dominic Meier Yvonne Anne Oswald Stefan Schmid Roger Wattenhofer. History of behavioural network models. Once upon a time... ... every node follows protocol malicious nodes selfish/rational nodes - PowerPoint PPT PresentationTRANSCRIPT
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On the Windfall of Friendship: Inoculation Strategies on Social Networks
Dominic Meier Yvonne Anne Oswald
Stefan SchmidRoger Wattenhofer
Yvonne Anne Oswald @ EC 2008
Once upon a time...
... every node follows protocol
• malicious nodes
• selfish/rational nodes
(game theory meets computer science)
History of behavioural network models
still no explanation for behaviour of real networks
now
Yvonne Anne Oswald @ EC 2008
“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)
New model: care about your friends’ wellbeing
neighbour pj
new equilibria (FNE)
Windfall of Friendship WoF(F) = cost(aworstNE)
cost(aworstFNE)
____________
4 Yvonne Anne Oswald @ EC 2008
Case study: virus inoculation game [Aspnes et al., SODA 2005]
social networks everywhere: facebook, co-authors, email ....
=> many connections
=> fast virus distribution
5 Yvonne Anne Oswald @ EC 2008
Virus inoculation game [Aspnes et al., SODA 2005]
social networks everywhere: facebook, co-authors, email ....
=> many connections
=> fast virus distribution
6 Yvonne Anne Oswald @ EC 2008
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
Virus Inoculation Game - Example
Yvonne Anne Oswald @ EC 2008
Virus Inoculation Game - Example
Yvonne Anne Oswald @ EC 2008
Virus Inoculation Game – Example
Yvonne Anne Oswald @ EC 2008
Virus Inoculation Game - Example
Yvonne Anne Oswald @ EC 2008
Virus Inoculation Game - Example
Yvonne Anne Oswald @ EC 2008
Virus Inoculation Game - Example
Yvonne Anne Oswald @ EC 2008
• 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
Model [Aspnes et al., SODA 2005]
Yvonne Anne Oswald @ EC 2008
strategies of pi
Actual cost [Aspnes et al., SODA 2005]
ai = 0 : device is not protected ai = 1 : device is protected
actual cost:
(per node)
C if ai = 1ca(i,a) =
L¢ ki/n if ai = 0
ki = size of attack component of pi
social cost
(network)
cost(a) = pi ca(i,a)
Yvonne Anne Oswald @ EC 2008
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
Introducing friendship
Windfall of Friendship WoF(F) = cost(aworstNE)
cost(aworstFNE)
____________
F 2 [0,1] Friendship Factor
perceived cost:
(per node)
cp(i,a) = ca(i,a) + F¢ pj neighbour ca(j,a)
cost(a) = pi ca(i,a)
Yvonne Anne Oswald @ EC 2008
General graphs
Results
• 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
PoA ≤ n[Aspnes et al., SODA’05]
Example
Yvonne Anne Oswald @ EC 2008
n = 13C = 1L = 4
WoF(F) is NOT monotonically increasing in F
total cost = 4.69social optimum
Yvonne Anne Oswald @ EC 2008
n = 13C = 1L = 4
WoF(F) is NOT monotonically increasing in F
total cost = 12.76selfish setting
PoA = 2.73
Yvonne Anne Oswald @ EC 2008
n = 13C = 1L = 4F = 0.9
WoF(F) is NOT monotonically increasing in F
total cost = 12.23friendly setting
WoF(0.9) = 1.04
Yvonne Anne Oswald @ EC 2008
WoF(F) is NOT monotonically increasing in F
total cost = 4.69n = 13C = 1L = 4F = 0.1
friendly setting
WoF(0.1) = 2.73
Yvonne Anne Oswald @ EC 2008
General graphs
Results
• 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
Results
complete graph • a FNE always exists, fast convergence
• WoF(F) ≤ 4/3 (tight)
star 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)
Special graphs
011)L/Cn1(F41F2
1F1L/Cn
Yvonne Anne Oswald @ EC 2008
Results
complete graph • a FNE always exists, fast convergence
• WoF(F) ≤ 4/3 (tight)
star 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)
Special graphs
Yvonne Anne Oswald @ EC 2008
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
There is nothing bad in being social, even for
computer scientists
and economists ...
Moral of the story
27 Yvonne Anne Oswald @ EC 2008
The End!
Thank you!
Questions? Comments?