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How Cooperation Arises in Evolving Social Networks
How Cooperation Arises in Evolving Social Networks
An Agent-Based Model
by Ariana Strandburg-Peshkin
An Agent-Based Model
by Ariana Strandburg-Peshkin
The Prisoner’s DilemmaThe Prisoner’s Dilemma
NetworksNetworks
Evolving NetworksEvolving Networks
Network Structure
Network Dynamics
The ModelThe Model
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2 , 2 0 , 3
3 , 0 1 , 1
A strategy - probability ofcooperating (0 - 1)
Links to other agents (“neighbors”)
Agents in a network playprisoners’ dilemma with all their “neighbors”
Agent 1 PayoffsC D
Age
nt 2
Pay
offs
D
C
Each agent has…
An Agent’s UniverseAn Agent’s Universe
Strategy
Payoff
Strategy
Payoff
Weight
Weight
Weight
Strategy
Payoff
Strategy
Payoff
Each Iteration…Each Iteration…Play all neighbors,
sum up total payoff, and update link weights
Find most successfulneighbor
Move towardmost successful
strategy
Break tieswith worst
enemy
Replenishties broken
ResultsResults
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Break ties --> Cooperate
No breaking ties --> Defect
Why?Why?
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Strategy
Link
s
Speed of ConvergenceSpeed of Convergence
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Probability of Breaking Ties Network Size (# agents) Network Density (# links)
Parameters Explored: Probability of Breaking Ties Network Size (# agents) Network Density (# links)
Time to Converge vs. Probability of Breaking Ties(25 Agents, 50 Links)
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability of Breaking Ties
Iterations until Average Strategy = .99
Time to Converge vs. Probability of Breaking Ties
y = 5271.2x -
0.7021
1000
10000
100000
1000000
0.01 0.1 1
Probability of Breaking Ties
Iterations until Average Strategy = .99
Time to Converge vs. Probability of Breaking Ties
1000
10000
100000
0.01 0.1 1
Probability of Breaking Ties
Time to Reach Average Strategy = .99 (Iterations)
Time to Converge vs. Network Size (Network Density = 2 Links /
0
20000
40000
60000
80000
100000
10 110 210 310 410 510 610 710
Agents
Iterations to Average Strategy = .99
Time to Converge vs. Number of Links
0
5000
10000
15000
20000
25000
0 20 40 60 80 100 120 140 160
Number of Links (Agents = 25)
Convergence Speed (Iterations to .99)
Results - SummaryResults - Summary
Networks with any probability of breaking ties eventually converge on cooperation
The speed of convergence depends on: Probability of breaking ties (> = faster) Size of network (> = slower) # of Links (> = slower)
Networks with any probability of breaking ties eventually converge on cooperation
The speed of convergence depends on: Probability of breaking ties (> = faster) Size of network (> = slower) # of Links (> = slower)
Implications / LimitationsImplications / 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)
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)
Other Cool Things To Look AtOther 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
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
SourcesSources Abramson, Guillermo, and Marcelo Kuperman. "Social games in a social network." Physical
Review E 63.3 (2001). 10 Apr. 2008 <http://arxiv.org/abs/nlin.AO/0010015>.
Calderon, Juan. "Games on Evolving Networks." Complex Systems Summer School at Santa Fe Institute. 18 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fwww.santafe.edu%2Fevents%2Fworkshops%2Fimages%2F6%2F6e%2FSf_csss06_calderon_et_al.pdf&ei=nbwcSI2XEJf4eZXdsOgL&usg=AFQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQ&sig2=ZGkomgzCTy37xNR9nb52Ew>.
Hanaki, Nobuyuki, Alexander Peterhansl, Peter Dodds, and Duncan Watts. "Cooperation in Evolving Social Networks." Management Science 53.7 (2007): 1036-1050. 19 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fcdg.columbia.edu%2Fuploads%2Fpapers%2Fhanaki_cooperation.pdf&ei=4JQaSLvBFJDqgwTQk6S4Dg&usg=AFQjCNF7aLFpLvwGQQdFQEtvy4BStmta4g&sig2=WSUWZyRpQRPt-9neDtyn-Q>.
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 <http://arxiv.org/abs/cond-mat?papernum=0308392>.
Ostrom, Elinor. "Collective Action and the Evolution of Social Norms." The Journal of Economic Perspectives 14.3 (2000): 137-158.
Abramson, Guillermo, and Marcelo Kuperman. "Social games in a social network." Physical Review E 63.3 (2001). 10 Apr. 2008 <http://arxiv.org/abs/nlin.AO/0010015>.
Calderon, Juan. "Games on Evolving Networks." Complex Systems Summer School at Santa Fe Institute. 18 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fwww.santafe.edu%2Fevents%2Fworkshops%2Fimages%2F6%2F6e%2FSf_csss06_calderon_et_al.pdf&ei=nbwcSI2XEJf4eZXdsOgL&usg=AFQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQ&sig2=ZGkomgzCTy37xNR9nb52Ew>.
Hanaki, Nobuyuki, Alexander Peterhansl, Peter Dodds, and Duncan Watts. "Cooperation in Evolving Social Networks." Management Science 53.7 (2007): 1036-1050. 19 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fcdg.columbia.edu%2Fuploads%2Fpapers%2Fhanaki_cooperation.pdf&ei=4JQaSLvBFJDqgwTQk6S4Dg&usg=AFQjCNF7aLFpLvwGQQdFQEtvy4BStmta4g&sig2=WSUWZyRpQRPt-9neDtyn-Q>.
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 <http://arxiv.org/abs/cond-mat?papernum=0308392>.
Ostrom, Elinor. "Collective Action and the Evolution of Social Norms." The Journal of Economic Perspectives 14.3 (2000): 137-158.
