How Cooperation Arises in Evolving Social Networks

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How Cooperation Arises in Evolving Social Networks

• An Agent-Based Model
• by Ariana Strandburg-Peshkin

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The Prisoners Dilemma
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Networks
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Evolving Networks
Network Structure
Network Dynamics
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The Model
Each agent has
A strategy - probability of cooperating (0 - 1)
Links to other agents (neighbors)
Agent 1 Payoffs
C
D
C
Agent 2 Payoffs
Agents in a network play prisoners dilemma with
all their neighbors
D
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An Agents Universe
Strategy Payoff
Weight
Strategy Payoff
Weight
Weight
Strategy Payoff
Strategy Payoff
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Each Iteration
Play all neighbors, sum up total payoff, and
update link weights
Find most successful neighbor
Replenish ties broken
Break ties with worst enemy
Move toward most successful strategy
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Results
Break ties --gt Cooperate No breaking ties --gt
Defect
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Why?
Links
Strategy
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Speed of Convergence

• Parameters Explored
• Probability of Breaking Ties
• Network Size ( agents)
• Network Density ( links)

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Results - Summary

• Networks with any probability of breaking ties
  eventually converge on cooperation
• The speed of convergence depends on
• Probability of breaking ties (gt faster)
• Size of network (gt slower)
• of Links (gt slower)

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Implications / Limitations

• Social punishment (by breaking ties) is
  effective in promoting cooperation
• Model requires that agents be intelligent and
  knowledgeable about one another
• Keep track of neighbors / weights
• Know neighbors strategies and payoffs
• No complex strategies (e.g. Tit-For-Tat)

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Other Cool Things To Look At

• Different Payoff Schemes
• More complex strategies
• Network Structure
• How is it affected by the game played?
• Cost of keeping so many ties? Cost of making and
  breaking ties?
• Robustness

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Sources

• Abramson, Guillermo, and Marcelo Kuperman.
  "Social games in a social network." Physical
  Review E 63.3 (2001). 10 Apr. 2008
  lthttp//arxiv.org/abs/nlin.AO/0010015gt.
• Calderon, Juan. "Games on Evolving Networks."
  Complex Systems Summer School at Santa Fe
  Institute. 18 Mar. 2008 lthttp//www.google.com/url
  ?satctrescd1urlhttp3A2F2Fwww.santafe.edu
  2Fevents2Fworkshops2Fimages2F62F6e2FSf_csss0
  6_calderon_et_al.pdfeinbwcSI2XEJf4eZXdsOgLusgA
  FQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQsig2ZGkomgzCTy3
  7xNR9nb52Ewgt.
• Hanaki, Nobuyuki, Alexander Peterhansl, Peter
  Dodds, and Duncan Watts. "Cooperation in Evolving
  Social Networks." Management Science 53.7 (2007)
  1036-1050. 19 Mar. 2008 lthttp//www.google.com/url
  ?satctrescd1urlhttp3A2F2Fcdg.columbia.ed
  u2Fuploads2Fpapers2Fhanaki_cooperation.pdfei4
  JQaSLvBFJDqgwTQk6S4DgusgAFQjCNF7aLFpLvwGQQdFQEtv
  y4BStmta4gsig2WSUWZyRpQRPt-9neDtyn-Qgt.
• Holme, Peter, Ala Trusina, Beon Jun Kim, and
  Petter Minnhagen. "Prisoners' Dilemma in
  Real-World Acquaintance Networks Spikes and
  Quasiequilibria Induced by the Interplay Between
  Structure and Dynamics." Physical Review E 68
  (2003). 10 Apr. 2008 lthttp//arxiv.org/abs/cond-ma
  t?papernum0308392gt.
• Ostrom, Elinor. "Collective Action and the
  Evolution of Social Norms." The Journal of
  Economic Perspectives 14.3 (2000) 137-158.