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Reputation Dynamics Through Gossiping
V.A. Traag1, P. Van Dooren1, Y.E. Nesterov2
1ICTEAM
Universit´e Catholique de Louvain
2CORE
Universit´e Catholique de Louvain
20 April 2012
Negative Ties and
Social Networks
Workshop
Motivation
Indirect reciprocity
• Indirect reciprocity ‘good’ explanation for human cooperation.
• Usual approach: reputation dynamics.
• Cavity: spreading of reputation tacitly assumed.
Gossiping, our approach
• Make spreading of reputation explicit: gossip.
• What is result of gossiping?
• Who will cooperate with whom?
Proposed model
Basics
1 Each agent has a reputation of the other: Rij(m)
2 Everybody plays and cooperates/defects based on local
reputation
3 Everybody gossips the result of the interaction
4 New reputation Rij(m + 1) based on:
◮ Own observation,
◮ Gossip.
Decision to cooperate
The decision to cooperate αij (m) =
0 if Rij (m) < 0
1 if Rij (m) ≥ 0
Gossiping
Consider all neighbours k when updating the reputation Rij
i j
k
The link to
be updated.
Does i ‘like’ k?
Will k gossip to i?
What action
has j taken
to k?
Social strategy
G B
C + −
D − +
Reputation of k, or αik(m).
Action of j, or αjk(m)
Action is considered as
either Good or Bad
Social strategy
• Cooperation vs. good agent and defection vs. bad agent is good
• Change in reputation due to gossiping with neighbour k
∆Sij (k, m) = αki (m)(2αik (m) − 1)(2αjk (m) − 1)
Individual strategy
C D
C + −
D − +
Action of j, or αji (m).
Action of j, or αij (m)
Action is considered as
either Good or Bad
Individual strategy
• +1 for ‘good’ actions, −1 for ‘bad’ actions to reputation
• We currently study WSLS-like: Consider CC and DD as good.
∆Iij (m) = (2αij (m) − 1)(2αji (m) − 1)
Reputation dynamics
Combine individual & social strategies
Combine with social influence parameter 0 ≤ λ ≤ 1
∆Rij (m) = (1 − λ)
Individual strategy
(2αij (m) − 1)(2αji (m) − 1) +
λ
1
n − 2
k=i,j
αki (m)(2αik (m) − 1)(2αjk (m) − 1)
Social strategy
Reputation dynamics
Rij(m + 1) = Rij(m) + ∆Rij(m)
Cooperative steady states
Steady states
• For which networks do we have αij (m + 1) = αij (m)?
• Good reputation remains good, bad reputation remains bad
Group structure
• Groups are stable steady states
• Cooperate within groups, defect between groups
• Implies it is (weakly) social balanced
• Can have q groups if
λ >
q
q + 1
More social influence may lead to more fragmented cooperation.
Social Balance
Why do dynamics promote weak social balance?
Change for high λ
∆Rij ∼
k:αki =1
(2αik − 1)(2αjk − 1).
• Become friends with similar people (αik = αjk).
• Become enemies with enemies of friends (αik = 1, αjk = 0)
• Don’t care about enemies of enemies (αik = 0)
• Essential: no communication between enemies.
Social Norm
Cooperation can be seen as social norm
Social Norm
• Cooperate with in-group, defect with others.
• If violated, reputation decreases: punishment.
• Other behaviour could be modeled similarly.
Example
Random initial state (p = 0.5)
Example
Random initial state (p = 0.5)
Example
Random initial state (p = 0.5) Final steady state
Evolutionary dynamics
Four different regimes (Cooperate with prob p on first round)
p < 1/2 p > 1/2
λ < 1/2 Individualistic prejudiced
• Defect vs. cooperators
• Cycles of cooperation vs.
defectors
Individualistic trusting
• Cooperate vs.
cooperators
• Cycles of cooperation
vs. defectors
λ > 1/2 Social prejudiced
• Cooperate vs. cooperators
(except second round)
• Defect vs. defectors
(except second round)
Social trusting
• Cooperate vs.
cooperators
• Defect vs. defectors
Phase portraits Individual
C D
Gossipers
Individual Prejudiced
C D
Gossipers
Individual Trusting
In ‘friendly’ environment, being individually prejudiced pays off.
Phase portraits Social
C D
Gossipers
Social Prejudiced
C D
Gossipers
Social Trusting
In ‘hostile’ environment, being socially trusting pays off.
Conclusions
Proposed model
• Proposed model for gossiping and reputation dynamics.
• Interesting connection with social balance.
• Can be evolutionary stable.
• Social influence does not necessarily improve cooperation
Thank you for your attention.
Questions?

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Reputation Dynamics Through Gossiping

  • 1. Reputation Dynamics Through Gossiping V.A. Traag1, P. Van Dooren1, Y.E. Nesterov2 1ICTEAM Universit´e Catholique de Louvain 2CORE Universit´e Catholique de Louvain 20 April 2012 Negative Ties and Social Networks Workshop
  • 2. Motivation Indirect reciprocity • Indirect reciprocity ‘good’ explanation for human cooperation. • Usual approach: reputation dynamics. • Cavity: spreading of reputation tacitly assumed. Gossiping, our approach • Make spreading of reputation explicit: gossip. • What is result of gossiping? • Who will cooperate with whom?
  • 3. Proposed model Basics 1 Each agent has a reputation of the other: Rij(m) 2 Everybody plays and cooperates/defects based on local reputation 3 Everybody gossips the result of the interaction 4 New reputation Rij(m + 1) based on: ◮ Own observation, ◮ Gossip. Decision to cooperate The decision to cooperate αij (m) = 0 if Rij (m) < 0 1 if Rij (m) ≥ 0
  • 4. Gossiping Consider all neighbours k when updating the reputation Rij i j k The link to be updated. Does i ‘like’ k? Will k gossip to i? What action has j taken to k?
  • 5. Social strategy G B C + − D − + Reputation of k, or αik(m). Action of j, or αjk(m) Action is considered as either Good or Bad Social strategy • Cooperation vs. good agent and defection vs. bad agent is good • Change in reputation due to gossiping with neighbour k ∆Sij (k, m) = αki (m)(2αik (m) − 1)(2αjk (m) − 1)
  • 6. Individual strategy C D C + − D − + Action of j, or αji (m). Action of j, or αij (m) Action is considered as either Good or Bad Individual strategy • +1 for ‘good’ actions, −1 for ‘bad’ actions to reputation • We currently study WSLS-like: Consider CC and DD as good. ∆Iij (m) = (2αij (m) − 1)(2αji (m) − 1)
  • 7. Reputation dynamics Combine individual & social strategies Combine with social influence parameter 0 ≤ λ ≤ 1 ∆Rij (m) = (1 − λ) Individual strategy (2αij (m) − 1)(2αji (m) − 1) + λ 1 n − 2 k=i,j αki (m)(2αik (m) − 1)(2αjk (m) − 1) Social strategy Reputation dynamics Rij(m + 1) = Rij(m) + ∆Rij(m)
  • 8. Cooperative steady states Steady states • For which networks do we have αij (m + 1) = αij (m)? • Good reputation remains good, bad reputation remains bad Group structure • Groups are stable steady states • Cooperate within groups, defect between groups • Implies it is (weakly) social balanced • Can have q groups if λ > q q + 1 More social influence may lead to more fragmented cooperation.
  • 9. Social Balance Why do dynamics promote weak social balance? Change for high λ ∆Rij ∼ k:αki =1 (2αik − 1)(2αjk − 1). • Become friends with similar people (αik = αjk). • Become enemies with enemies of friends (αik = 1, αjk = 0) • Don’t care about enemies of enemies (αik = 0) • Essential: no communication between enemies.
  • 10. Social Norm Cooperation can be seen as social norm Social Norm • Cooperate with in-group, defect with others. • If violated, reputation decreases: punishment. • Other behaviour could be modeled similarly.
  • 13. Example Random initial state (p = 0.5) Final steady state
  • 14. Evolutionary dynamics Four different regimes (Cooperate with prob p on first round) p < 1/2 p > 1/2 λ < 1/2 Individualistic prejudiced • Defect vs. cooperators • Cycles of cooperation vs. defectors Individualistic trusting • Cooperate vs. cooperators • Cycles of cooperation vs. defectors λ > 1/2 Social prejudiced • Cooperate vs. cooperators (except second round) • Defect vs. defectors (except second round) Social trusting • Cooperate vs. cooperators • Defect vs. defectors
  • 15. Phase portraits Individual C D Gossipers Individual Prejudiced C D Gossipers Individual Trusting In ‘friendly’ environment, being individually prejudiced pays off.
  • 16. Phase portraits Social C D Gossipers Social Prejudiced C D Gossipers Social Trusting In ‘hostile’ environment, being socially trusting pays off.
  • 17. Conclusions Proposed model • Proposed model for gossiping and reputation dynamics. • Interesting connection with social balance. • Can be evolutionary stable. • Social influence does not necessarily improve cooperation Thank you for your attention. Questions?