In social simulation, not only is the structure of the social relations fundamental for the construction of plausible scenarios, but also the interaction processes are shaped by such structures. Each actor interacts in multiple social contexts located within multiple social relations that constitute their social space. We build on previous work about context switching to study the notion of context segregation. The agents not only switch between social contexts, carrying with them their unique social identity, but also choose the contexts according to personal reasons. We apply the notion of context segregation to a simple game of consensus in which agents try to collectively achieve an essentially arbitrary consensus. We make a first analysis of our set of experiments towards understanding the influence of the segregation mechanism in the speed of convergence to global consensus and compared the results with the context switching model.

1. Consensus by segregation - the formation of local
consensus within context switching dynamics
Davide Nunes, Luis Antunes
GUESS / LabMAg / University of Lisbon, Portugal
{davide.nunes, xarax}@di.fc.ul.pt
September 7, 2012
WCSS 2012

2. Outline
1 Introduction
2 Multi-context Models
Consensus
Context Permeability
On Context Switching
A Model of Context Segregation
3 Model of Experiments
4 Preliminary Model analysis
Context Tolerance Analysis
Switching mechanism trends
5 Conclusion and Future Work

3. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Social Spaces
In real world scenarios, agents interact in multiple complex social
relations with other agents and/or institutions.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 3 / 22

4. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Social Spaces
In real world scenarios, agents interact in multiple complex social
relations with other agents and/or institutions.
Social Space
Davide Nunes, Luis Antunes (GUESS) WCSS2012 3 / 22

5. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Social Spaces
In real world scenarios, agents interact in multiple complex social
relations with other agents and/or institutions.
Social Space
Provides Structure, fundamental for the construction of
plausible interaction scenarios
Davide Nunes, Luis Antunes (GUESS) WCSS2012 3 / 22

6. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Social Spaces
In real world scenarios, agents interact in multiple complex social
relations with other agents and/or institutions.
Social Space
Provides Structure, fundamental for the construction of
plausible interaction scenarios
Shape the interaction processes
Davide Nunes, Luis Antunes (GUESS) WCSS2012 3 / 22

7. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Social Spaces
In real world scenarios, agents interact in multiple complex social
relations with other agents and/or institutions.
Social Space
Provides Structure, fundamental for the construction of
plausible interaction scenarios
Shape the interaction processes
Highly contextual
Davide Nunes, Luis Antunes (GUESS) WCSS2012 3 / 22

8. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Problems of current modeeling approaches
Davide Nunes, Luis Antunes (GUESS) WCSS2012 4 / 22

9. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Problems of current modeeling approaches
To collapse the complexity of social relations into a single
relation depicted in a bi-dimensional space or a single social
network is overly simplistic.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 4 / 22

10. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Problems of current modeeling approaches
To collapse the complexity of social relations into a single
relation depicted in a bi-dimensional space or a single social
network is overly simplistic.
It may jeopardise the quality of simulation results and
undermine the confidence in the derived conclusions and their
applicability.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 4 / 22

11. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Multiple context Models
Social relations may be of different kind and quality,
possessing different topologies and social dynamics.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 5 / 22

12. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Multiple context Models
Social relations may be of different kind and quality,
possessing different topologies and social dynamics.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 5 / 22

13. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Multiple context Models
Social relations may be of different kind and quality,
possessing different topologies and social dynamics.
We model social spaces with multiple concurrent social
networks [3, 1, 2].
Davide Nunes, Luis Antunes (GUESS) WCSS2012 5 / 22

14. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Multiple context Models
Social relations may be of different kind and quality,
possessing different topologies and social dynamics.
We model social spaces with multiple concurrent social
networks [3, 1, 2].
These networks represent abstract social relations.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 5 / 22

15. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Multiple context Models
Social relations may be of different kind and quality,
possessing different topologies and social dynamics.
We model social spaces with multiple concurrent social
networks [3, 1, 2].
These networks represent abstract social relations.
Research Context
We focus on the study of dynamic consequences of the topological
structures underlying social simulation scenarios.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 5 / 22

16. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

17. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
The agent society is trying to achieve arbitrary global
consensus
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

18. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
The agent society is trying to achieve arbitrary global
consensus
The agents must choose between two possible choices
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

19. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
The agent society is trying to achieve arbitrary global
consensus
The agents must choose between two possible choices
In each iteration of the game:
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

20. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
The agent society is trying to achieve arbitrary global
consensus
The agents must choose between two possible choices
In each iteration of the game:
1 each agent selects an available neighbour
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

21. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
The agent society is trying to achieve arbitrary global
consensus
The agents must choose between two possible choices
In each iteration of the game:
1 each agent selects an available neighbour
2 an agent observes the choice adopted by the neighbour
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

22. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
Consensus Game
The agent society is trying to achieve arbitrary global
consensus
The agents must choose between two possible choices
In each iteration of the game:
1 each agent selects an available neighbour
2 an agent observes the choice adopted by the neighbour
3 the agent decides to switch its choice if the newly observed
choice represents the majority
Davide Nunes, Luis Antunes (GUESS) WCSS2012 6 / 22

23. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

24. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Problem - Self Reinforcing Substructures
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

25. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Problem - Self Reinforcing Substructures
Daniel Villatoro, “Social Norms for Self-Policing Multi-agent
Systems and Virtual Societies”
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

26. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Problem - Self Reinforcing Substructures
Daniel Villatoro, “Social Norms for Self-Policing Multi-agent
Systems and Virtual Societies”
groups of nodes that, given the appropriate configuration of
agent preferences and network topology, do maintain sub
conventions
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

27. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Problem - Self Reinforcing Substructures
Daniel Villatoro, “Social Norms for Self-Policing Multi-agent
Systems and Virtual Societies”
groups of nodes that, given the appropriate configuration of
agent preferences and network topology, do maintain sub
conventions
present in network models like BA scale-free networks
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

28. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Problem - Self Reinforcing Substructures
Daniel Villatoro, “Social Norms for Self-Policing Multi-agent
Systems and Virtual Societies”
groups of nodes that, given the appropriate configuration of
agent preferences and network topology, do maintain sub
conventions
present in network models like BA scale-free networks
modelling social spaces with a single network containing these
structures prevents the convergence to global consensus
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

29. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Consensus
The emergence of conventions
Consensus games can be regarded as a process of abstract
convention emergence.
Problem - Self Reinforcing Substructures
Daniel Villatoro, “Social Norms for Self-Policing Multi-agent
Systems and Virtual Societies”
groups of nodes that, given the appropriate configuration of
agent preferences and network topology, do maintain sub
conventions
present in network models like BA scale-free networks
modelling social spaces with a single network containing these
structures prevents the convergence to global consensus
This phenomenon was also confirmed in all our previous work
[1, 2, 3]
Davide Nunes, Luis Antunes (GUESS) WCSS2012 7 / 22

30. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Permeability
Context Permeability
Davide Nunes, Luis Antunes (GUESS) WCSS2012 8 / 22

31. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Permeability
Context Permeability
Our previous work on context permeability [3, 1] explored an
agent-based model in which agents interact in multiple social
networks at the same time playing the consensus game.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 8 / 22

32. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Permeability
Context Permeability
Our previous work on context permeability [3, 1] explored an
agent-based model in which agents interact in multiple social
networks at the same time playing the consensus game.
This provided some basis for the exploration of the
permeability phenomena.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 8 / 22

33. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Permeability
Context Permeability
Our previous work on context permeability [3, 1] explored an
agent-based model in which agents interact in multiple social
networks at the same time playing the consensus game.
This provided some basis for the exploration of the
permeability phenomena.
Social Permeability
Davide Nunes, Luis Antunes (GUESS) WCSS2012 8 / 22

34. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Permeability
Context Permeability
Our previous work on context permeability [3, 1] explored an
agent-based model in which agents interact in multiple social
networks at the same time playing the consensus game.
This provided some basis for the exploration of the
permeability phenomena.
Social Permeability
Social Contexts can overlap providing a context permeability
phenomena.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 8 / 22

35. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Permeability
Context Permeability
Our previous work on context permeability [3, 1] explored an
agent-based model in which agents interact in multiple social
networks at the same time playing the consensus game.
This provided some basis for the exploration of the
permeability phenomena.
Social Permeability
Social Contexts can overlap providing a context permeability
phenomena.
This social world feature is of extreme importance for the
dissemination of phenomena, and societal adaptiveness.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 8 / 22

36. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Context Switching
The context switching model
We explore the previous idea of context permeability in what
regards to the temporal dynamics of multiple social contexts.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 9 / 22

37. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Context Switching
The context switching model
We explore the previous idea of context permeability in what
regards to the temporal dynamics of multiple social contexts.
In this model agents interact in one context at the time.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 9 / 22

38. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Context Switching
The context switching model
We explore the previous idea of context permeability in what
regards to the temporal dynamics of multiple social contexts.
In this model agents interact in one context at the time.
Agents switch their context after each interaction based on a
switching probability ζ.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 9 / 22

39. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Context Switching
The context switching model
We explore the previous idea of context permeability in what
regards to the temporal dynamics of multiple social contexts.
In this model agents interact in one context at the time.
Agents switch their context after each interaction based on a
switching probability ζ.
Temporal Context Permeability
some contexts can overlap providing permeability throughout
different temporal instances
Davide Nunes, Luis Antunes (GUESS) WCSS2012 9 / 22

40. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
On Context Switching
Example of Context Switching
Figure : Example of context switching [2] considering two contexts for
social agent denoted by the number 1. In this case, these contexts are
created by two distinct physical spaces. Common nodes in both
neighbourhoods (like agent 2) represent an acquaintance of actor 1 in
both of them. The dashed circle represents the scope of each context.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 10 / 22

41. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
A Model of Context Segregation
A Model of Context Segregation
We extend the previous context switching model with a
segregation mechanism.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 11 / 22

42. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
A Model of Context Segregation
A Model of Context Segregation
We extend the previous context switching model with a
segregation mechanism.
We add a new parameter of social tolerance µ.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 11 / 22

43. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
A Model of Context Segregation
A Model of Context Segregation
We extend the previous context switching model with a
segregation mechanism.
We add a new parameter of social tolerance µ.
Questions
Does the formation of local consensus groups foster a faster
convergence to global consensus?
What are the dynamics to be expected from strategic context
switching by a segregation process?
Davide Nunes, Luis Antunes (GUESS) WCSS2012 11 / 22

44. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
A Model of Context Segregation
Context Segregation Example
Context 1
Tolerance: 0.5
c Time: t
d
a b
t + 1 - switching by
segregation
Context 2
Tolerance: 0.5
Time: t
c
d
a b
Figure : At the end of the simulation iteration t, agent a has to decide
whether to switch context or not. The current context for agent a has a
tolerance of µC1 = 0.5. As the ratio of neighbours with an opposite
choice is above the tolerance threshold, the agent will become active in
context 2 at time t + 1.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 12 / 22

45. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Model of Experiments
Each experiment consists of 30 runs in which 300 agents
interact until 3000 cycles pass, or total consensus is reached.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 13 / 22

46. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Model of Experiments
Each experiment consists of 30 runs in which 300 agents
interact until 3000 cycles pass, or total consensus is reached.
Our goal is to analyse the influence of the new parameter (the
context tolerance µCi ) in the speed of convergence to global
consensus measured in terms of the number of encounters
necessary.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 13 / 22

47. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Model of Experiments
Each experiment consists of 30 runs in which 300 agents
interact until 3000 cycles pass, or total consensus is reached.
Our goal is to analyse the influence of the new parameter (the
context tolerance µCi ) in the speed of convergence to global
consensus measured in terms of the number of encounters
necessary.
tolerance parameter span from 0 to 1 in intervals of 0.05.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 13 / 22

48. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Model of Experiments
Each experiment consists of 30 runs in which 300 agents
interact until 3000 cycles pass, or total consensus is reached.
Our goal is to analyse the influence of the new parameter (the
context tolerance µCi ) in the speed of convergence to global
consensus measured in terms of the number of encounters
necessary.
tolerance parameter span from 0 to 1 in intervals of 0.05.
switching probability parameter ζCi varied between three
values that were found to be interesting for the context
switching mechanism [2].
Davide Nunes, Luis Antunes (GUESS) WCSS2012 13 / 22

49. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Preliminary Model analysis
We have analysed the response surfaces for the tolerance
parameter span
Davide Nunes, Luis Antunes (GUESS) WCSS2012 14 / 22

50. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Preliminary Model analysis
We have analysed the response surfaces for the tolerance
parameter span
We conducted different experiments varying the switching
probability to observe the interplay between these two
parameters.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 14 / 22

51. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Preliminary Model analysis
We have analysed the response surfaces for the tolerance
parameter span
We conducted different experiments varying the switching
probability to observe the interplay between these two
parameters.
We vary the network topologies experimenting with both
homogeneous and heterogeneous social contexts.
Davide Nunes, Luis Antunes (GUESS) WCSS2012 14 / 22

52. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Tolerance Analysis
Homogeneous Social Contexts: scale-free networks
1.0
1.0
0
00
0
20
1600
20
0
16000
1600
00
20000
0.8
0.8
0
1600 1800
0
0
18
14000 25000
00
0
0
25000 00
0.6
0.6
14
Avg.
Avg.
20000
20000
14
Enco
0
1400
Enco
0.4
0.4
00
1.0 1.0
12000
1
1
0
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ntext
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0.8 0.8
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unter
00
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for Co
10000 12000 10000
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0.2
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1.0 1.0 14
0
0.4 0.4
00
00
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16000
0.8
ance
ance
18
0
0
Tole 0.6 Tole 0.6 16
0.2 0.2
0
00
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Toler
0
Toler
e fo e fo
16
1600
0.0
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onte 0.00.0 onte 0.00.0
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0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
(a) (ζC1 , ζC2 ) = (0.25, 0.25) (b) (ζC1 , ζC2 ) = (0.5, 0.5)
1.0
0
26
00
22000 28
00
26
00
0
0.8
0
0
00
40000
24
20 24000
00
35000 0
0.6
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Avg.
22
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unter
20000 0.8
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0.6 16000 16000
15000 20
00
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e fo
0.0
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onte 0.00.0
xt 2
0.0 0.2 0.4 0.6 0.8 1.0
(c) (ζC1 , ζC2 ) = (0.75, 0.75)
Davide Nunes, Luis Antunes (GUESS) WCSS2012 15 / 22

53. Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work
Context Tolerance Analysis
Heterogeneous Social Contexts: scale-free + k-regular
networks
1.0
1.0
0
00
12000 10
12000
10000
10000
0.8
0.8
8000
20000
20000 8000
6000
Avg.
0.6
0.6
Avg.
15000
Enco
15000
Enco
unter
0.4
0.4
1.0 1.0
1
1
10000
unter
10000
ntext
ntext
0.8 6000 0.8
6000
s
6000
s
0.6 for Co 0.6
for Co
5000
0.2
0.2
1.0 0.4 1.0 0.4
0.8 0.8 8000
8000 10000
ance
ance
0.6 0.6 1000
Tole 0.2 Tole 0.2 0
ranc 0.4 1200 ranc 0.4
Toler
10000 000
Toler
e fo e fo 0
0 1600
0.0
0.0
rC 0.2 12 rC 0.2
onte 0.00.0 onte 0.00.0
xt 2 xt 2
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
(d) (ζC1 , ζC2 ) = (0.5, 0.5) (e) (ζC1 , ζC2 ) = (0.5, 0.5)
and k = 10 and k = 30
1.0
10000
10000
0.8
25000 8000
6000
0.6
20000
Avg.
Enco
15000
0.4
1.0
xt 1
unter
10000 0.8
Conte
6000
s
5000 0.6
8000
0.2
1.0
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0.4
0.8 1200 0
ance
Tole 0.6
0.2 0 1200
ranc 0.4
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1600
0.0
rC 0.2
onte 0.00.0
xt 2
0.0 0.2 0.4 0.6 0.8 1.0
(f) (ζC1 , ζC2 ) = (0.5, 0.5)
and k = 50
Davide Nunes, Luis Antunes (GUESS) WCSS2012 16 / 22