Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer...
-
Upload
kathy-summerfield -
Category
Documents
-
view
216 -
download
0
Transcript of Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer...
![Page 1: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/1.jpg)
Evolving Cooperation in the N-player Prisoner's
Dilemma: A Social Network Model
Dept Computer Science and Software Engineering
Golriz Rezaei Michael Kirley
Jens Pfau
ACAL09 Conference – practice talk Oct 2009
![Page 2: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/2.jpg)
Motivation
The Dilemma: - Contribution to the social community beneficial for everybody - Autonomous self-interested individuals rational, maximize their utility
“Tragedy of the Commons” [Hardin 1968 science] - Theoretical biology / Game theory they should “Defect” - Nature / Reality they “Cooperate”
Important Question in many areas :
How/Why does cooperation emerge? What about Artificial Multi-agent systems?
Frame work: N-player Dilemma games on social groups.
Distributed Artificial Intelligence (DAI) Physics (Statistical Physics) Biology (Theoretical biology, Nature) Evolutionary Computation (IEEE Trans, CEC) Multi agent systems (AAMAS)
![Page 3: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/3.jpg)
Overview
What is a social network Brief overview of Prisoner’s Dilemma
(N-player PD game) PD on network Proposed model Evaluation by experiments Conclusion Questions
![Page 4: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/4.jpg)
Complex Networks every where
Social Networks
Networks
Topology Function
Social ties Behaviour
![Page 5: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/5.jpg)
Network Basics
Network graph, G(N, E), N finite set of nodes (vertices) E finite set of edges (links) G represented by N×N adjacency matrix
aij = 1 there is an edge between node i and j
aij = 0 otherwise
![Page 6: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/6.jpg)
Examples of Social Net
Internet-Map
![Page 7: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/7.jpg)
Red, blue, or green: departments Yellow: consultants
Grey: external expertswww.orgnet.com
Structure of an organization
![Page 8: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/8.jpg)
Topological properties
Degree, ki , of a node
Path length, L average separation between any two nodes
Clustering coefficient, Ci , of a node
probability that two nearest neighbours of a node are also nearest neighbours of each other.
N
jjiE
0
![Page 9: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/9.jpg)
Prisoner’s Dilemma (2 players)
(D,D) Nash Equilibrium
Ccooperate
DDefect
Ccooperate
b-c -c
DDefect
b 0
• 2 players / agents• 2 choices (C or D)• Payoff joint actions
![Page 10: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/10.jpg)
N-Player Prisoner’s Dilemma
Natural extension
Utility [Boyd and Richerson 1988 J. Th. Biology]
Conditions defection is preferred for individuals
contribution to social welfare is beneficial for the group
Conventional EG (D,D, … all D)
0 cb
Nbc /
![Page 11: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/11.jpg)
PD on Spatial structure
Local neighbourhood interaction
Clusters of cooperators
Enhance cooperation
![Page 12: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/12.jpg)
Related work
• Santos Et. Al. [2009 Nature]Heterogeneous graphs (number and size of the game)
Promotes cooperation
• Ohtsuki Et. Al. [2006 Nature] Correlation cost and benefit & the underlying connectivity of agents
• Ellis & Yao [2007 IEEE CEC] Reputation mechanism reputation scores embedded in social
network
![Page 13: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/13.jpg)
Contribution - Hypothesis
Introducing more cognitive agents (base their decision on some function of the opponents)
Incorporating “social network” into N-player PD (network evolves by cooperative behaviour)
Encourage high levels of cooperation Persist for longer Analyse the state of underlying network
![Page 14: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/14.jpg)
Proposed model
Algorithm: Social network based N-PD modelRequire: Population of agents P, iteration = imax, players N 2
1: for i = 0 to imax do2: G = 0;3: while g = NextGame(P,G, N) do4: G = G {g}5: PlayGame(g)6: AdaptLinks(g)7: end while8: a,b = Random Sample(P)9: CompareUtilityAndSelect(a,b)10: end for
Decision
How
![Page 15: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/15.jpg)
Game Execution
Two scenarios (cognitive abilities)Pure strategy (always cooperate/defect)
Mixed strategy (play probabilistically)
Based on a function of average links weight ( )(β generosity)(α gradient of the function)
– Agents receive corresponding payoff based on outcomes (Boyd and Richerson function)
Decision
)(gWi
![Page 16: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/16.jpg)
Link adaptation
Agents play cooperatively form social links (reinforced)
One agent defects breaks his links with the opponents
How
slow positive / fast negative
![Page 17: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/17.jpg)
Snapshots of the model
Self-organize social ties based on their self-interest
Strategy update cultural evolution
(a) Iteration 5 (b) Iteration 100 (c) Iteration 1000
![Page 18: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/18.jpg)
Experimental Setup
population size = 1000 ε = 0.9 (game formation) b = 5 and c = 3 (payoff values benefit & cost) pure strategy scenario (50% pure C – 50% pure D) mixed strategy scenario (33.3% each) α = 1.5 and β = 0.1 (decision function) average20 independent trials up to 40000 iterations
What is the equilibrium state and network topology?
![Page 19: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/19.jpg)
Experiment 1 Group size vs. Strategy
2
4
5
10 15 20
2
4
5
10
15
20
Pure strategy Mixed strategy
Rat
io o
f Coo
pera
tion
Rat
io o
f Coo
pera
tion
Time (iteration) Time (iteration)
![Page 20: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/20.jpg)
Experiment 2 Emergent social networks
Pure strategy Mixed strategy
2
4
510 15 20
24
5
10
15
20
Clu
ste
r C
oe
ffici
en
t
Clu
ste
r C
oe
ffici
en
t
Time (iteration) Time (iteration)
![Page 21: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/21.jpg)
Experiment 3 Final Degree Distribution
N = 2 N = 10
log(k) log(k)
log
(P(k
))
log
(P(k
))
![Page 22: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/22.jpg)
Conclusion
– Results validate the hypothesis
Incorporating “social network” into N-player PD
encourage high levels of cooperation and persist for longer– Social nets important in promoting and sustaining
cooperation (specially with cognitive agent)– Endogenous network formation – Analysis of the emergent social networks
high average clustering broad-scale heterogeneity
– Local structure hierarchical organization of cooperation
![Page 23: Evolving Cooperation in the N-player Prisoner's Dilemma: A Social Network Model Dept Computer Science and Software Engineering Golriz Rezaei Michael Kirley.](https://reader038.fdocuments.us/reader038/viewer/2022102923/551b388c550346d41a8b5297/html5/thumbnails/23.jpg)
Questions?
Thank you