The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with...
Transcript of The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with...
![Page 1: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/1.jpg)
0 - ETH Colloquium ‘07 (Zurich)
The Wisdom of Networked Agents
Akira NamatameNational Defense Academy of Japan
www.nda.ac.jp/~nama
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1 - ETH Colloquium ‘07 (Zurich)
Low
Low
High
High
Scale
Multi-agentsystems
Socio physics(Complex networks)
M&S in social systems
Game theory
Self-interest seeking Adaptability
RESEARCH MAP
Social atom:Not observe individual behaviorbut observe patterns
Complex adaptive systems
<particle> <agent>
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2 - ETH Colloquium ‘07 (Zurich)
Networked worlds:
Everything is connected!
Two phases in networks(1) Phase with positive network effects
: More people means more benefits
(2) Phase with negative network effects
: More persons begin to decrease the value of a network result from resource limits
(traffic congestion, network service overloads)
Why Do Things Get Worse?
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3 - ETH Colloquium ‘07 (Zurich)
Outline
• Social Interaction with Externalities• Consensus Problems on Complex Networks : Flock of moving agents• Social Choice as Consensus Formation• Collective Decisions with Externalities
: Sequential Decisions and Cascade: Repeated Games on Networks
• Congestion Control of Networked Agents
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4 - ETH Colloquium ‘07 (Zurich)
• Crowds are often foolishHuman beings loose their rationality in a crowd
Crowd psychology: herding, cascade, group think,…
Madness of Crowds
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5 - ETH Colloquium ‘07 (Zurich)
A large collection of people are smarter than an elite few. J. Surowiecki,(2004) suggests new insights regarding how our social and
economic activities should be organized.: The wisdom of crowds emerges only under the right conditions
(diversity, independence, etc)
The Wisdom of Crowds
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Dual Phases in Collective Behaviour
Disconnected agents Connected agents
We study interaction and the underlying network topology that flip between two phases
: Under what mechanism can we improve collective behaviour?: Under what mechanism can we improve collective behaviour?
: The key point is to characterize : The key point is to characterize interactionsinteractions among agentsamong agents
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7 - ETH Colloquium ‘07 (Zurich)
Types of Social Interaction (1)
Type 1: Coordination problems: Consensus problem (control theory): Synchronization (physics/complex networks)
: Herding (economics/psychology) : Social choice (social sciences) : Coordination games (game theory)
Type 2: Dispersion problems: Congestion control (engineering) : Stock markets (economics): Minority games (econophysics)
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8 - ETH Colloquium ‘07 (Zurich)
Mixture of coordination and dispersion problems(1) Economics:Tug-of-war between increasing returns and decreasing returns
(2) Social sciences: Reconcile the tension between centripetal and centrifugal
(population dynamics, city development)
(3) Human behaviors: Mixture of conformists and non-conformists: Tension between rational agents and irrational agents
Types of Social Interaction (2)
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9 - ETH Colloquium ‘07 (Zurich)
Outline
• Social Interaction with Externalities• Consensus Problems on Complex Networks
: Flock of moving agents• Social Choice as Consensus Formation• Collective Decisions with Externalities
: Sequential Decisions and Cascade: Repeated Games on Networks
• Congestion Control of Networked Agents
![Page 11: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/11.jpg)
10 - ETH Colloquium ‘07 (Zurich)
Consensus Problems
Consensus means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents. A consensus algorithm is a decision rule that results in the convergence of the states of all network nodes to a common value.
[01]: Olfati-Saber 2007
Source: Olfati-Saber 2007 [C1]
xi = xj = …= xconsensus
Convergence of the states of all agents to a common value
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11 - ETH Colloquium ‘07 (Zurich)
The Role of Network Topology in Consensus Problems
The distributed algorithm for consensus problems
The weighted adjacency matrix G=(wij)
(i) Graph G is connected(ii)G is balanced: symmetric graph ∑∑ ≠≠
=ij jiji ij ww
))()(()()1( txtxwtxtx iNi
jijiii
−+=+ ∑∈
ε
nxxxxi in /)0(...21 ∑====
Thorem: (A. Jadbaie, 2006)The algorithm converges to the average of the initial values ofall agents if the underlying graph G is connected and balanced
Agents adjust the states to those of their neighbors.
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12 - ETH Colloquium ‘07 (Zurich)
Synchronization Problems
“Emergence of flocking behavior”
Vicsek T,.Phys Rev Letter (1995)
““Consensus has connections to synchronization problemsConsensus has connections to synchronization problems””
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13 - ETH Colloquium ‘07 (Zurich)
Synchronization in Globally Connected Networks
Observation:Observation:No matter how large the network is, a globally coupled network will synchronize if its coupling strength is sufficiently strong
Good – if synchronization is useful
G. Ron Chen (2006)G. Ron Chen (2006)
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14 - ETH Colloquium ‘07 (Zurich)
Synchronization in Locally Connected NetworksSynchronization in Locally Connected Networks
Observation:Observation:No matter how strong the coupling strength is, a locally coupled network will not synchronize if its size is sufficiently large
Good - if synchronization is harmful
G. Ron Chen (2006)G. Ron Chen (2006)
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15 - ETH Colloquium ‘07 (Zurich)
SynchronizationSynchronization in Small-World Networks
Start from a nearest neighbor coupled network
Add a link, with probability p, between a pair of nodes
Good news
X.F.Wang and G.R.Chen: Int. J. Bifurcation & Chaos (2001)
: : A small-world network is easy to synchronize!!
small-world networkG. Ron Chen (2006)G. Ron Chen (2006)
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16 - ETH Colloquium ‘07 (Zurich)
Synchronization and Underlying Network Topology
λ1 = 0 is always an eigenvalue of a Laplacian matrixλN/λ2:algebraic connectivity is a good measure of synchronization.
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−
nk
kk
}1,0{
}1,0{
2
1
Oλ2 = 0.238 λ2 = 0.925
Laplacian matrix = Degree – Adjacency matrix
Laplacian matrixNetwork A Network B
Connectivity of networks determines synchronization
Fiedler, “Algebraic connectivity of graphs,”
Czechoslovak Mathematical Journal, 1973, 23: 298-305
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17 - ETH Colloquium ‘07 (Zurich)
A B
Close, but not too closefar away
too close
Flock: Mixture of Coordination and Dispersion
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18 - ETH Colloquium ‘07 (Zurich)
Flock with BOID Model
Craig W. Reynolds (1994)
Cohesion Separation Alignment
•Cohesion: Head for the perceived center of mass of the neighbors. •Separation: Don't get too close to any object.•Alignment: Try to match the speed and direction of nearby neighbors.
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19 - ETH Colloquium ‘07 (Zurich)
Vcs
0
0.2
0.4
0.6
0 1 2 3 4 5
D
Emergence of Flock with Self-Control Rules
Self-control by minimizing the implicit potential function
cohesion, separation
VaDs
caisicifi eweDwwFFFF rrrrrr
+⎟⎠⎞
⎜⎝⎛ −=++=
DwDw scfi log−=φ
alignment
c
s
ww
<Force of an agent>
c
sn
jij w
wdDti
→=⇒∞→ ∑r
0→=⇒∞→ ∑in
jijvVt r
∞→tBalance between attractiveforce and repulsive force
Consensus: converge to the same velocity
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20 - ETH Colloquium ‘07 (Zurich)
Constrained Flock (1)
Force of flocking movement:Force of moving for destination: invoked with some probability p:
fFr
dFpr
flocking movement force
totalFr
dFpr
fFr
Flock moving toward a given destination
combined force: dftotal FpFFrrr
+=
force for destination
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21 - ETH Colloquium ‘07 (Zurich)
Constrained Flock (2): Avoiding an Obstacle
with probabilistic invoke: p=0.15
Break Away
without probabilistic invoke: p=1 Dead Lock
destination
dftotal FpFFrrr
+=
critical parameter value: pc=0.15
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22 - ETH Colloquium ‘07 (Zurich)
Phase Transition in Network Topology:Connection Probability
p = 10-4 p = 10-3
p: connection probability to others (remote link)
disconnected agents connected agents
critical parameter value: pc= 10-3
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23 - ETH Colloquium ‘07 (Zurich)
Triplets Phases in Network Topologies
random graph small-world graph
random remote link
local links
densely connected
connected graph
random remote link
disconnected agents agents in flock
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24 - ETH Colloquium ‘07 (Zurich)
p
p
p
d: Average links (degree)
dmax : N-1 (complete graph)
Phase Transition in Flocking: Substrate Networks
complete graph
small-world type
random graph
connection probability (remote link)
no flocking
Flocking is emerged
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25 - ETH Colloquium ‘07 (Zurich)
Outline
• Social Interaction with Externalities• Consensus Problems on Complex Networks
: Flock of moving agents• Social Choice as Consensus Formation• Collective Decisions with Externalities
: Sequential Decisions and Cascade: Repeated Games on Networks
• Congestion Control of Networked Agents
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26 - ETH Colloquium ‘07 (Zurich)
The Stock Market as Beauty Contest
Keynes remarked that the stock market is like a beauty contest. “General theory of Employment Interest and Money”. (1936)
: Keynes had in mind contests that were popular in England at the time, where a newspaper would print 100 photographs, and people would write in which six faces they liked most.
: Everyone who picked the most popular face was automatically entered in a raffle, where they could win a prize.
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27 - ETH Colloquium ‘07 (Zurich)
Beauty Contest as Social Choice•There is the set of alternatives to be ranked.•Each member has his/her preference. •The society have to decide ordering on all alternatives, which is the best, the second best,and so on.
Preference aggregationPreference
aggregation
Individual preferences
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28 - ETH Colloquium ‘07 (Zurich)
Social Choice with Voting
Voting is the archetypical form of making a social decision.
Preference aggregationAggregate individual preferences on the set of alternatives to obtain a “social ordering”.
KENNETH J. ARROW (1951): No voting scheme over three or more alternatives can satisfies all of reasonable and logical conditions.
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29 - ETH Colloquium ‘07 (Zurich)
Paradox of Voting: Condorcet (1785)Binary choice: No problem with votingHow to extend the idea with more than two choices?
➭The problem known as “paradox of voting.”:Three candidates: {a, b, c}, Preference of three voters : {A, B, C} A: B: C:
Group choice:
α
cb ffα acb ff bac ff
acb fffα
a b c
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30 - ETH Colloquium ‘07 (Zurich)
Borda Count (1770)
Each voter submits a complete ranking of all the m candidatesFor each voter that places a candidate first, that candidate receives m-1 points, for each voter that place her 2nd place receives m-2 points, and so forth.The candidate with the highest Borda count wins
Preference of three voters
cba ff
acb ff
bac ff
Borda count:
a: 6, b: 6, c: 6
(paradox of voting)
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31 - ETH Colloquium ‘07 (Zurich)
Forward and Inverse Problems in Social Systems
preference adaptation
Forward problem
Aggregatedpreference
Aggregatedpreference
<Inverse problem>
How agents preferences should be adapted for better social choice?
Inverse problem
<Forward problem>
How social choice should be maid by aggregating individual preferences?
Agents specify complete preferencesAggregate all preferences and announce it all agentsAgents modify original preferences
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32 - ETH Colloquium ‘07 (Zurich)
Group Preference and Indexing with Borda Count
Group preference
C 2
C nC 1
preference
O α
Oβ
(Oα is preferred to Oβ)
βα
βα
OOthenn
OC
n
OCif
n
i
in
i
i
f )()(
1
)(
1
)( ∑∑== <
Each agent has an ordered list of alternatives
Compute the rank of the alternative
Rank order the alternative according to the decreasing sum of their ranks
O2
O 1
O4
O3
O5
10000
11000
11010
10100
11001
Preference index
54321 ,,,, ooooo
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33 - ETH Colloquium ‘07 (Zurich)
Consensus Formation of Adaptive Agents
α
: aggregated preference of choice j (borda score)
: preference of agent i on choice j.
: adaptation level (social influence )
)()()1()( ααα OGOCOC jiji +−=
)( jOG
)( ji OC
Adaptive model of Individual preference:
“Agents concern both own preferences and group preference”
Preference modification
Aggregatedpreference
Aggregatedpreference
)( jOG
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1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
2
1
3
5
4
5
1
4
3
2
Agen t 1 Agen t 5Agen t 4Agen t 3Agen t 2
Agent preferences (paradox of voting occurs)
Agent1:0.9
Agent5:0.1
Agent4:0.3
Agent3:0.5
Agent2:0.7
1 2 3 4 5
1
2
3
4
5
α of A gent
Initial group preference
derived group preference
Simulation Setting
Agent1:0.1
Agent5:0.1
Agent4:0.1
Agent3:0.1
Agent2:0.11 2 3 4 5
α of A gent Initial group preference
derived group preference
1 2 3 4 5
Group B: adaptation levels are high and different
Consensus was not reached
}5,...,2,1:{ : }5,...,2,1:{ :
====
iOWesalternativFiveiAGagentsFive
i
i
Group A: adaptation level is low and the same
Consensus was reached
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(Borda count of each alternative)
(Each score of alternatives are same. =Ordering of alternatives was fail. )
Group A: Consensus was not reached
Group B: Consensus was reached. 43215 ooooo ffff
![Page 37: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/37.jpg)
36 - ETH Colloquium ‘07 (Zurich)
Fallacies of Composition and Division
: The fallacy of composition and the fallacy of division involve parts and wholes.
: The fallacy of composition occurs when we assume that a whole has a property that it's parts do.
: The fallacy of division runs in the opposite direction. It occurs when we assume that the parts of a thing have the sameproperties as the whole.
: The fallacies arise because wholes often have emergent properties that their parts lack, and parts often have adaptive properties that do not belong to the whole that they constitute.
![Page 38: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/38.jpg)
37 - ETH Colloquium ‘07 (Zurich)
Outline
• Social Interaction with Externalities• Consensus Problems on Complex Networks
: Flock of moving agents• Social Choice as Consensus Formation• Collective Decisions with Externalities
: Sequential Decisions and Cascade: Repeated Games on Networks
• Congestion Control of Networked Agents
![Page 39: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/39.jpg)
38 - ETH Colloquium ‘07 (Zurich)
Social Networks as Complex Systems
• Interactions are more important than individual behaviour
• How do interactions influence rational behaviour?
<madness of crowds>People follow the herdEasier to follow than to thinkIf one does it, others followFashionsPanic in emergenciesPeer pressureThe snowball effect
![Page 40: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/40.jpg)
39 - ETH Colloquium ‘07 (Zurich)
Factors that Influence on Social Complex Systems
Social pressureAGENT
Social network changes an agent’s behaviour
(1) Preference heterogeneity(2) Social influence (3) Social network: Degree heterogeneity
Preference
Preference determines an agent’s behaviour
Social pressure influences an agent’s behaviour
Social network
![Page 41: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/41.jpg)
40 - ETH Colloquium ‘07 (Zurich)
Restaurant A
Restaurant B
Which restaurant should I choose ?
How other peoples have chosen?
Agents make decisions in order
agents who prefer A
agents who prefer B
Sequential Decisions and CascadeDecision externalities
![Page 42: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/42.jpg)
41 - ETH Colloquium ‘07 (Zurich)
Binary Choice under Social Influence (1)
0
1.2
-6 -4 -2 0 2 4 6
q
UA – UB
SellBuy
Probability to buy: p1
•Probability to choose A
q = 1 / (1+exp(-(UA -UB)))
•Probability to choose B
1-q = 1 / (1+exp(-(UB- UA)))
Logit Model
P(t+1): the probability to choose A at time t+1
)()()1()1( tSUqtp αα +Δ−=+
S(t):the proportion of the agents who have chosen S1 by t
10 ≤≤ α
Utility UA Utility UB
α :social influence level
social influenceindividualpreference
![Page 43: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/43.jpg)
42 - ETH Colloquium ‘07 (Zurich)
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
α
σ2 /N mean
min
max
agent number:1000initial condition: M(0)=N(0)=1
Collective Behavior of Conformists: Agent Preference vs. Social Pressure
Cascade level
∑=
−=N
ttS
1
22 ))(( μσ
social influence level
S(t)=M(t)/{(M(t)+N(t)}: the ratio of agents who have chosen A by time t
:A half of agents prefer A to B and the rest of agents prefer B to A
5.0=μ
Cascade occurs under strong social influence
)()()1()1( tSUqtp αα +Δ−=+
![Page 44: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/44.jpg)
43 - ETH Colloquium ‘07 (Zurich)
Agent Heterogeneity and Cascade
Conformist: Prefers the majority choice (a longer queue)
Restaurant A
Restaurant B
Non-conformist: Prefers the minority choice (a shorter queue)
)()()1()1( tSUqtp αα +Δ−=+
))(1()()1()1( tSUqtp −+Δ−=+ αα
A mixed population of conformists and non-conformists
Balance between centripetal (conformist) and centrifugal (non-conformist)
social influence invokes the opposite direction
![Page 45: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/45.jpg)
44 - ETH Colloquium ‘07 (Zurich)
∑=
−=N
t
tS1
22 ))(( μσ
Collective Decision: A Mixed Population of Conformists and Non-conformists
social influence level
ratio of non-conformist
: Large cascade caused under strong social influence(However strong individual preference mitigates cascade): Non-conformists stabilize collective decision: Cascade does not occur when 20% of agents are non-conformists(Cascade is mitigated by a small fraction of irrational agents)
αθ
Cascade level
![Page 46: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/46.jpg)
45 - ETH Colloquium ‘07 (Zurich)
Outline
• Social Interaction with Externalities• Consensus Problems on Complex Networks
:Flock of Moving Agents• Consensus Formation
: Social Choice of Networked Agents • Collective Decisions with Externalities
: Sequential Decisions and Cascade: Repeated Games on Complex Networks
• Congestion Control of Networked Agents
![Page 47: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/47.jpg)
46 - ETH Colloquium ‘07 (Zurich)
Beauty Contest Games
<Payoff scheme>
Coordination game: An agent wins if his choice is the same as the majority choice
Dispersion game: An agent wins if his choice is the same as the minority choice
1− θ
θ
An agent bits one unit by splitting 1− θ on S1 and θ on S2
S1
S2
S1 S2
S1 0S2 0
θ−1
θ
S1 S2
S1 0S2 0
θ−1θ
Coordination game Dispersion game
![Page 48: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/48.jpg)
47 - ETH Colloquium ‘07 (Zurich)47
Simulation Setting: Majority GameAgent preference level: θ
Agent heterogeneity: the density of θ: f(θ)
Aggregated choicep
5.0<θ5.0>θ
: prefer S1 : prefer S2
θ>)(tp
θ<)(tp: choose S1 : choose S2
An agent’s best-response rule
p: the proportion of agents to choose S1
S1 S2
S1 0S2 0
θ−1
θCoordination game
![Page 49: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/49.jpg)
48 - ETH Colloquium ‘07 (Zurich)
Collective Dynamics with Hub Agents
Impact of hub agentsPeer influence
symmetric interaction (degree) asymmetric interaction (degree)
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49 - ETH Colloquium ‘07 (Zurich)49
Social Interaction ModelsHub Model
Hub Model: Collective decision with opinion leaders (hub agent): Hub agent i adapts to the aggregated information of subgroup i: All other agents adapt to 4 local neighbors as well as the hub agents
Hub agent 1 Hub agent 2
Aggregate Information
Global model:(mean-filed model)
Local model
![Page 51: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/51.jpg)
50 - ETH Colloquium ‘07 (Zurich)50
Global Model vs. Local Model
Initial proportion of S1
◆: Global model▲: Local model (4 neighbors)
proportion of S1
(1) p(0) <0.25, p(0)>0.75:
coexistence of the two opinions
(2) 0.25 < p(0) < 0.75:
0
0.25
0.5
0.75
1
0 0.25 0.5 0.75 1p(0)
p*
●: S1●: S2●: S1⇔S2●: S2⇔S1
Local model
Consensus on one opinion
converges to one opinion
critical point: initial ratio at p(0)=0.5global model
Global model
p*=0.5
Local model
Coexistence different opinions
![Page 52: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/52.jpg)
51 - ETH Colloquium ‘07 (Zurich)51
Frangible Collective Decision with Hub Agents
Hub agents destabilize collective decision
0
0.25
0.5
0.75
1
0 0.25 0.5 0.75 1p(0)
p*
Hub Model
proportion of S1
Case 1:Interact with only a hub agent
●: S1●: S2●: S1⇔S2●: S2⇔S1
Case 2:Interact with both a hub agent and neighbors
Hub1 Hub 2
Group 1 Group 2
p*: 0.5⇔1.0
p*=0.5
![Page 53: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/53.jpg)
52 - ETH Colloquium ‘07 (Zurich)
Outline
• Social Interaction with Externalities• Consensus Problems on Complex Networks
: Flock of moving agents• Social Choice as Consensus Formation• Collective Decisions with Externalities
: Sequential Decisions and Cascade: Repeated Games on Networks
• Congestion Control of Networked Agents
![Page 54: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/54.jpg)
53 - ETH Colloquium ‘07 (Zurich)
Smart Agents Using ICT(ICT:Information/Communication
Technology)
![Page 55: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/55.jpg)
54 - ETH Colloquium ‘07 (Zurich)
Congestion control should receive much attention
uncontrolled system
EFF
ICIE
NC
Y
controlled system
PROBLEM CAUSED BY CONGESTION
Loss of efficiency
Unfair allocation of resources among competing usersideal
LOADCritical load
Why Do Things Get Worse (cont.)?
![Page 56: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/56.jpg)
The queuing is one of the greatest invention
![Page 57: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/57.jpg)
56 - ETH Colloquium ‘07 (Zurich)
Queuing Discipline: FIFO
First-In-First-Out (FIFO)• most widely used discipline• first customer that arrives is the first one to be
serviced (or transmitted)Madness of crowds
Wisdom of crowds
![Page 58: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/58.jpg)
57 - ETH Colloquium ‘07 (Zurich)
Internet Traffic DynamicsQuestions
: How does the network topology influence the traffic dynamics?
: How does user heterogeneity influence the traffic dynamics?
Heavy users send or down load extremely big files
![Page 59: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/59.jpg)
58 - ETH Colloquium ‘07 (Zurich)
Performance Evaluation via Simulation
networksimulation
• user heterogeneity(file size distribution)
traffic demand
congestioncontrol
performancemeasures
networktopology
• connectivity• bandwidths
• TCP flow• drop tail, red,..
• throughput• packet drop rate
throughput=file size/time to be sent
![Page 60: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/60.jpg)
59 - ETH Colloquium ‘07 (Zurich)
Uncontrolled vs. Controlled Particles
agent agent
self-controlled particles
uncontrolled particles ・UDP Flow: open-loop flow
U
in flow current flow
X
H
U X-
+
・TCP Flow: closed-loop flow
Gcurrent flowin flow
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60 - ETH Colloquium ‘07 (Zurich)
Traffic Dynamics on an Open-Loop System
David Arrowsmith, 2006
![Page 62: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/62.jpg)
61 - ETH Colloquium ‘07 (Zurich)
Little’s Law
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62 - ETH Colloquium ‘07 (Zurich)
Critical Load of an Open-Loop Traffic System
![Page 64: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/64.jpg)
63 - ETH Colloquium ‘07 (Zurich)Packet rate
ScaleScale--free:free:κ=2κ=2
Random networkRandom network
Del
iver
ed p
acke
ts
ScaleScale--free:free:κ=3κ=3
Random network outperforms scale-free network without congestion control
Network Performance: Uncontrolled Traffic Flow
![Page 65: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/65.jpg)
64 - ETH Colloquium ‘07 (Zurich)
Active Queue management (AQM): the traffic of each link is controlled by the router
Congestion Analysis of Controlled Flow
AQM: Drop tail, RED, CHOKE
![Page 66: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/66.jpg)
65 - ETH Colloquium ‘07 (Zurich)
TCP Congestion Control
Window algorithm:send W packets at a time
• increase window size W by one per RTT if no loss, : W <- W+1 each RTT
• decrease window size by half on detection of loss : W <− W/2
sender
receiver
W
AIMD: Additive Increase Multiplicative Decrease
RTT: round trip time
![Page 67: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/67.jpg)
66 - ETH Colloquium ‘07 (Zurich)
Random networkRandom network
ScaleScale--freefree
Scale-free network outperforms random network with congestion control
low traffic heavy traffic
Traffic Dynamics on a Closed-Loop System
![Page 68: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/68.jpg)
67 - ETH Colloquium ‘07 (Zurich)
Tiers(96 ’ M.B.Doar)
Transit-Stub model
(96’ Ellen W)
Barabasi-Albert model
Hierarchy: Tree Scale Free
Traffic Dynamics: Substrate Network
WAN,MAN,LAN ISP NetworkAutonomous systems
Modular network
![Page 69: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/69.jpg)
68 - ETH Colloquium ‘07 (Zurich)
High Performance of Scale-free Network with Congestion Control
Edge betweennessNumber of hops
Complementary CDF(CCDF)
Distribution of hops
Scale free (BA) modelTiers modelTS model
Distributions of hops (average shortest paths) and edge betweenness
![Page 70: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/70.jpg)
69 - ETH Colloquium ‘07 (Zurich)
1 0-1
1 00
1 01
1 02
1 03
1 04
1 0-6
1 0-5
1 0-4
1 0-3
1 0-2
1 0-1
1 00
x
1-F(
x)
C o m p le m e n ta ry C u m u la tiv e D is tr ib u tio n P lo t
P a re to ( in f in ite v a r ia n c e )E x p o n e n tia l (f in ite v a r ia n c e )
Traffic Dynamics: User Heterogeneity
The file size distribution is scale-free (mixture of heavy users and light users): constant: normal distribution: exponential distribution: power-law distribution
IP Flow Size
file size
Complementary CDF
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70 - ETH Colloquium ‘07 (Zurich)
Tiers
Low traffic: Average size: 30kbyte
Comparison of Network Performances(Light Traffic Phase)
TS
Scale free
throughput
throughput=file size/time to be sent
:constant
:normal distribution
:exponential distribution
:power-law distribution
The network performance depends on theuser heterogeneity(the file size distribution)rather than the network topology
Complementary CDF(CCDF) of throughput
![Page 72: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/72.jpg)
71 - ETH Colloquium ‘07 (Zurich)
Tiers TS
Complementary CDF(CCDF) of Throughput Heavy traffic:Average size: 300kbyte
Comparison of Network Performances (Heavy Traffic Phase)
throughput
The network performance depends on thethe network topology rather than user heterogeneity(the file size distribution)
Scale free
![Page 73: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/73.jpg)
72 - ETH Colloquium ‘07 (Zurich)
1
)(1
+=
−=
α
α
α
αx
xPDF
xxCDF
m
m
β
β
β
β
M
M
xx
xx
CDF
1
)(
−
=
=
1+α1−β
log
logthroughput
Double Pareto Law
left side right side
throughput=file size/time to be sent
Power-law distribution has heavy-tail at the right side
Double Pareto law has heavy-tails at the both sides, left and right.
![Page 74: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/74.jpg)
73 - ETH Colloquium ‘07 (Zurich)
Double Pareto Law at Congestion Phase (1)
TS Model:
exponential
power law
File size distribution:constant File size distribution
normal distribution
Heavy traffic:average size: 300kbyte
![Page 75: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/75.jpg)
74 - ETH Colloquium ‘07 (Zurich)
Double Pareto Law at Congestion Phase (2)
Scale free network:
power law
File size distribution: constant
exponential
Heavy traffic:average size: 300kbyte
File size distribution normal distribution
![Page 76: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/76.jpg)
75 - ETH Colloquium ‘07 (Zurich)
Congestion Control Needs to Receive Much Attention
log
log
low rank
high rank
allocated resource
The distribution of throughput has heavy-tails at the both sides, left and right.
Double Pareto law: “The richer gets richer and the poorer gets more poor”
![Page 77: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/77.jpg)
76 - ETH Colloquium ‘07 (Zurich)
Summary: Incentive ControlGeneral problem: given a good social model, determine how to change social system behavior to optimize a system performance.In many social systems, intervention (control) can impact the outcome.Decentralized mechanism design with incentive control(guided self-organization)Typical setting:• Agents act in their own best interest with a partial
global view. • Agents can be given incentives to change behavior
Mixture of economics, game theory, computer science, statistical physics, and complex networks.
![Page 78: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/78.jpg)
77 - ETH Colloquium ‘07 (Zurich)
Challenging Issue:Why Do Things Get Worse?
Selection maintains stability at a local optimum
Balance phase Variation phaseEvolution
Exploration
Disturbance
Unbalanced system
Pressure towards stability
- modifies components- modifies relationships- modifies external systemsStable system
Dual Phase Evolution in Social Systems: DPE
(David Green, 2007)
![Page 79: The Wisdom of Networked Agentsnama/Top/InvitedTalk/07-05_it.pdfcoupled network Add a link, with probability p, between a pair of nodes Good news X.F.Wang and G.R.Chen: Int. J. Bifurcation](https://reader033.fdocuments.net/reader033/viewer/2022060502/5f1c5173e2c0197d912abef1/html5/thumbnails/79.jpg)
78 - ETH Colloquium ‘07 (Zurich)
Thank you for listening!!
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79 - ETH Colloquium ‘07 (Zurich)
Agent Heterogeneity and Cascade (1)
p(t+1): Probability to choose A at time t+1
10
M(t): the number of agents who have chosen A by time tN(t): the number of agents who have chosen B by time tS(t)=M(t)/{(M(t)+N(t)}: the ratio of agents who have chosen A
≤≤ α :social influence level
α=0: Logit model
α=1: Pure cascade model
)()()1()1( tSUqtp αα +Δ−=+
Population of agents
Prefer A
B
Prefer B
Aindividualpreference
social influence