The Theory of Social Interaction and Social Engineering - National

94 Pages·2007·2.77 MB·English

The Theory of Social Interaction
and Social Engineering
Akira Namatame
National Defense Academy of Japan
www.nda.ac.jp/~nama
0 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Related Disciplines
Scale of problem
High
Agents in a
Socio physics
(Complex networks) connected world
Multi-agent
systems
Game theory
Low
Low High
Self-interest seeking Selfish agent
Social atom
of elements
1 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Outline
• Social Interaction with Externality
• Social Dynamics on Complex Networks
• Computational Social Choice
• Beauty Contest Games
• Serendipity: Innovation and Diffusion on Networks
• Social Engineering
2 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Externalities: Network Effects
Networked worlds:
Everything is connected!
Positive and negative network effects
• Positive networks effects are obvious
: More people means more benefits
Negative network effects result from resource limits
: More persons begin to decrease the value of a network
(daily-life traffic conestions or network overloads)
Big question: How to measure network externalities?
3 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Types of Social Interaction
Type 1: Accumulation problems (positive network effects)
(cid:140)
Agents have tendency to take the same action.
: Consensus problem (control theory)
: Synchronization (physics/complex networks)
: Herding (economics/psychology)
: Gossip algorithm (computer science)
: Coordination game (game theory)
Type 2: Dispersion problems (negative network effects)
(cid:140)
Agents have tendency the distinct actions.
: Congestion problem (control theory)
: Minority games (econophysics)
Type 3: Mixed problems (both positive and negative network
(cid:140)
effects)
4 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Dynamics of Social Atoms
Universal social phenomena
No individual
People follow the herd
(cid:140)
preference
: Fashions
Social
Social
: Panic in emergencies
influence
atom
If one does it, others follow
(cid:140)
Social pressures influence
agent’s behaviour
Why?
(cid:140)
: Social pressure
: Easier to follow than to think
5 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Consensus, Herding, Cascade with the Voter Model
Behavioral rule
: Each site of a graph is endowed with two states – spin up ↑
(σ=+1) and down ↓(σ= -1) like the Ising model
: For each evolution time step,
i) pick a random site
ii) the selected site adopts the state of a randomly chosen
neighbor
iii)These steps are repeated until a finite system necessarily
reaches consensus
6 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Consensus Problems in Engineering
Consensus means to reach an agreement regarding a
(cid:140)
certain quantity of interest that depends on the state of
all agents.
More specific, a consensus algorithm is a decision rule
(cid:140)
that results in the convergence of the states of all
network nodes to a common value.
Convergence of the states of all agents to a common value
x = x = …= x
i j consensus
[01]: Olfati-Saber 2007
7 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Source: Olfati-Saber 2007 [C1]
Consensus on Dynamic Complex Networks
Dynamic Network of “agents”
(cid:140)
• Entities may be mobile
• Communication topology might be time-varying
The distributed consensus algorithm
∑
x (t +1) = x (t) +ε w (x (t) − x (t))
i i ij j i
i∈N
i
The weighted adjacency matrix G=(w )
ij
(i) Graph G is connected
(ii) G is balanced: ∑ w = ∑ w
ij ji
i≠ j j≠i
Convergence to the average of the initial values of all agents
∑
x = x = ... = x = x (0) / n
1 2 n i
i
8 -ABM-S4-ESHIA ‘07 (Agelonde, France)
Consensus under Partial Control
A new methodology in
(cid:140)
“Coordination and control of multiple agents”.
2
1
3
7 External
9
control
8
Consensus formation with partial control
4
6 5
Consensus formation
9 -ABM-S4-ESHIA ‘07 (Agelonde, France)