the prisoner's dilemma and social networks
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Using Diffusion Characters for the Taxonomy of Self-Organizing Social NetworksDaniel Ashlock and Colin LeeCIBCB 2009
Outline
Evolving social networks with unknown behaviour
Prisoner's Dilemma
Comparing similarity of emergent networks
Diffusion character algorithm
Similarity taxonomy
Future Work
Network comparison
Prisoner's Dilemma
20 000
Prisoner's Dilemma
10k
10k
cooperation
Prisoner's Dilemma
10k
10k
5k
5k
cooperation
defection
Prisoner's Dilemma
0k
20k
sucker!
temptation
5k
5k
defection
10k
10k
cooperation
Prisoner's Dilemma
Sucker Defection Cooperation Temptation
2 x Cooperation Sucker + Temptation
10k
10k
0k
cooperation
sucker!
temptation
5k
5k
defection
20k
Evolving Prisoners
Additionally:Agents can choose their conspiratorsBased on expectation
Offers of conspiracy can be rejectedOffering agent receives rejection payout
Wallflowers can refuse all offers and receive a wallflower payout
Highest scores after 150 rounds continues to next generation
Contact Networks
Using final generation of evolved agents
Contact number = number of times agents play one another
95% of mean contact number places an edge between agents
Contact Networks
Diffusion Characters
Comparing the similarity of networks
Technique: column entropy (CE) distance
Adjacency matrixDiffusion CharactermatrixColumn EntropyVector
Column EntropyVectorColumn EntropyVector Sort
distance
...
...
Diffusion Character Matrices
Adjacency matrix
Multiply by diffusion ( = )
Take Leontief inverse
Adjacency matrixDiffusion CharactermatrixColumn EntropyVector
Column EntropyVectorColumn EntropyVector Sort
distance
...
...
Leontief Inverse
Economicscalculate the total amounts of goods and services required for the production of one unit of output
!
(I T)-1I: identity matrix
T: adjacency matrix * diffusion
Adjacency matrixDiffusion CharactermatrixColumn EntropyVector
Column EntropyVectorColumn EntropyVector Sort
distance
...
...
Column Entropy distance
Normalize columns
Calculate column entropies
Sort entropy vectors
Euclidean distance between vectors
Adjacency matrixDiffusion CharactermatrixColumn EntropyVector
Column EntropyVectorColumn EntropyVector Sort
distance
...
...
Taxonomy of DC Distance
Evaluated:Visually in spring layout
Using fitness trajectories
Exploratory classification
Future work
Do the network comparisons work on large networks?
Use other ways to verify taxonomy data?
Collaborate??