How Cooperation Arises in Evolving Social Networks An Agent-Based Model by Ariana Strandburg-Peshkin.

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Transcript How Cooperation Arises in Evolving Social Networks An Agent-Based Model by Ariana Strandburg-Peshkin.

How Cooperation Arises in
Evolving Social Networks
An Agent-Based Model
by Ariana Strandburg-Peshkin
The Prisoner’s Dilemma
Networks
Evolving Networks
Network Structure
Network Dynamics
The Model
Each agent has…
A strategy - probability of
cooperating (0 - 1)
Links to other agents
(“neighbors”)
Agents in a network play
prisoners’ dilemma with all
their “neighbors”
Agent 2 Payoffs
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Agent 1 Payoffs
C
D
C
D
2,2
0,3
3,0
1,1
An Agent’s Universe
Strategy
Payoff
Weight
Strategy
Payoff
Strategy
Weight
Weight
Payoff
Strategy
Payoff
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
Results
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Break ties --> Cooperate
No breaking ties --> Defect
Links
Why?
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Strategy
Speed of Convergence
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Parameters Explored:
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Probability of Breaking Ties
Network Size (# agents)
Network Density (# links)
Time to Conv erge vs. Probability of Breaking Ties
(25 Agents, 50 Links)
180000
Iterations until Average Strategy = .99
160000
140000
120000
100000
80000
60000
40000
20000
0
0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
Probabilit y of Breaking Ties
0 .7
0 .8
0 .9
1
Time to Conv erge vs. Probability of Breaking Ties
Iterations until Average Strategy = .99
1000000
100000
10000
-
y = 5 2 7 1 .2 x
0.7021
1000
0 .0 1
0 .1
Probabilit y of Breaking Ties
1
Time to Conv erge vs. Probability of Breaking Ties
Time to Reach Average Strategy = .99 (Iterations)
100000
10000
1000
0 .0 1
0 .1
Probabilit y of Breaking Ties
1
Time to Conv erge vs. Network Size
(Network Density = 2 Links /
Iterations to Average Strategy = .99
100000
80000
60000
40000
20000
0
10
110
210
410
310
A gent s
510
610
710
Time to Conv erge vs. Number of Links
Convergence Speed (Iterations to .99)
25000
20000
15000
10000
5000
0
0
20
40
60
80
100
Number of Links (A gents = 25)
120
140
160
Results - Summary
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Networks with any probability of breaking
ties eventually converge on cooperation
The speed of convergence depends on:
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Probability of breaking ties (> = faster)
Size of network (> = slower)
# of Links (> = slower)
Implications / Limitations
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Social “punishment” (by breaking ties) is
effective in promoting cooperation
Model requires that agents be intelligent
and knowledgeable about one another
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Keep track of neighbors / weights
Know neighbors’ strategies and payoffs
No complex strategies (e.g. Tit-For-Tat)
Other Cool Things To Look At
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Different Payoff Schemes
More complex strategies
Network Structure
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How is it affected by the game played?
Cost of keeping so many ties? Cost of making
and breaking ties?
Robustness
Sources

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%2Fe
vents%2Fworkshops%2Fimages%2F6%2F6e%2FSf_csss06_calderon_et_al.pdf&ei=nbwcSI2X
EJf4eZXdsOgL&usg=AFQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQ&sig2=ZGkomgzCTy37x
NR9nb52Ew&gt;.

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%2F
uploads%2Fpapers%2Fhanaki_cooperation.pdf&ei=4JQaSLvBFJDqgwTQk6S4Dg&usg=AFQj
CNF7aLFpLvwGQQdFQEtvy4BStmta4g&sig2=WSUWZyRpQRPt-9neDtyn-Q&gt;.

Holme, Peter, Ala Trusina, Beon Jun Kim, and Petter Minnhagen. "Prisoners' Dilemma in RealWorld 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.