The Theory of Social Interaction and Social Engineeringnama/Top/InvitedTalk/07-04_it.pdf0 -...

0 - ABM-S4-ESHIA ‘07 (Agelonde, France)

The Theory of Social Interaction and Social Engineering

Akira NamatameNational Defense Academy of Japan

www.nda.ac.jp/~nama


Low

Low

High

High

Scale of problem

Multi-agentsystems

Socio physics(Complex networks)

Agents in a connected world

Game theory

Selfish agentSelf-interest seeking of elements

Social atom

Related Disciplines


Outline

• Social Interaction with Externality• Social Dynamics on Complex Networks• Computational Social Choice• Beauty Contest Games• Serendipity: Innovation and Diffusion on Networks• Social Engineering


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?

Externalities: Network Effects


Types of Social Interaction

Type 1: Accumulation problems (positive network effects)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)

Agents have tendency the distinct actions. : Congestion problem (control theory) : Minority games (econophysics)Type 3: Mixed problems (both positive and negative network effects)


Dynamics of Social Atoms

Social influence

Social

atomSocial pressures influence

agent’s behaviour

Universal social phenomena

People follow the herd

: Fashions

: Panic in emergencies

If one does it, others follow

Why?

: Social pressure

: Easier to follow than to think

No individual preference


Consensus, Herding, Cascade with the Voter Model

: 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 siteii) the selected site adopts the state of a randomly chosen neighboriii)These steps are repeated until a finite system necessarilyreaches consensus

Behavioral rule


Consensus Problems in Engineering

Consensus means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents. More specific, 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


Consensus on Dynamic Complex Networks

Dynamic Network of “agents”

• Entities may be mobile• Communication topology might be time-varying

The distributed consensus algorithm

The weighted adjacency matrix G=(wij)(i) Graph G is connected(ii)G is balanced: ∑∑ ≠≠

=ij jiji ij ww

))()(()()1( txtxwtxtx iNi

jijiii

−+=+ ∑∈

ε

nxxxxi in /)0(...21 ∑====

Convergence to the average of the initial values of all agents


7

12

3

4

56

89

A new methodology in“Coordination and control of multiple agents”.

Consensus under Partial Control

Consensus formation

Consensus formation with partial controlExternalcontrol


Outline

• Social Interaction with Externality• Social Dynamics on Complex Networks• Computational Social Choice• Beauty Contest Games• Serendipity: Innovation and diffusion on networks• Social Engineering


Contagion Models

The SIR model Consider a fixed population of size NEach individual is in one of three states:• Susceptible (S), Infected (I), Removed (R)

S I Rλ β

Dynamic contagion process: Mixing modelAt each time step, each individual comes into contact with another individual chosen uniformly at random

j

i


Universal Property of Contagion Models

Critical mass: threshold property in social dynamics

•Global Infection only occur after a threshold (critical mass)

•Many models on epidemic spreads, information cascades, fads, have the same threshold property

•susceptible become infected through their contacts with infected individuals at a rate

•Infected agents are removed at rate

β

•There is a threshold above which the

•diseases spread through the population

cλγβ

=

cλ

γ

•The network topology affects critical mass


Consensus Herd, Cascade on Social Networks

Recently much attention has been paid to complex networks as the skeleton of complex phenomena:

• Small world networks;• Scale-free networks;• Regular networks, random networks…

For simple propagation -such as the spread of information, disease, or rumor- in which a single infected node is sufficient to infect its neighbors, random links connecting distant nodes facilitate the propagation by creating “shortcuts” across the graph.


ρ

λλ c

disease spreadsdisease diesλ c =

<k2><k>

Example: Underlying Network Topology Influences Critical Mass

The critical mass is given at

<k>: average degree of node

Random & SW networks

Scale-free networks

Scale-free network does not have critical mass


Time to Reach Consensus: Voter Model

Intuitive: the time to reach complete ordering issmaller for the small-world (SW) network than for a regular lattice with the same number of nodes

Counterintuitive: during most of the evolution,nA is higher on the small-world (SW) network than on a regular lattice, for a long time interval, more disordered, and orders rapidly only at the very end

SW network

regular lattice

Slower is faster on the small-world (SW) networks!!

C. Castellano et al., Europhys. Lett. 63, 153 (2003)

nA:proportion of A


Consensus and SynchronizationConsensus and Synchronization

“Emergent behavior on flocks”

Vicsek T,.Phys Rev Letter (1995)

““Consensus has connections to problem in synchronizationConsensus has connections to problem in synchronization””


Synchronization in Globally Connected NetworksSynchronization 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)


SynchronizationSynchronization in Locally Connected Networksin 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)


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)


Synchronization: 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 does matter for synchronization

Fiedler, “Algebraic connectivity of graphs,”

Czechoslovak Mathematical Journal, 1973, 23: 298-305


Summary: Dynamics of Social Atoms

Social influence

Social atom

Main Issues Discussed

Critical mass phenomena

How is critical mass affected?

Coexistence of different opinions

Time to reach consensus

No individual preference


Collective Decision: Naive Assumption

Each agent chooses randomly and independent of all others.Collective decision: sum of all individual choices.

For binary choice voting:For binary choice voting:i)Individual agents: S = 0 or 1 i)Individual agents: S = 0 or 1 ii)Collective decision: M = ii)Collective decision: M = ΣΣ S S iii)Result: should be normal iii)Result: should be normal distribution.distribution.

NO YES

0 % Collective Decision M 100%


The Problem of Collective Decision(1)Emergence in the collective decision process

Example: Movie rankings according to votes by IMDB Example: Movie rankings according to votes by IMDB users.users.

In a society of agents free to choose, but they are constrained by limited information and having heterogeneous beliefs.

SitabhraSitabhra SinhaSinha (2005)(2005)

Long-tail Two-peaks


F. Schweitzer (2006)

The Problem of Collective Decision(2)


Interaction among AgentsModeling social phenomena : Emergence of collective properties from agent-level interactions.Approach : Social dynamics with interacting agents

: The agents easily synchronize their decisions.

(1) Weisbuch-Stauffer Model (2003)

: Agents interact with their ‘neighbors’ and their own belief.

(2) Denis-Gordon Model (2007)

: Agents have preference (willingness to pay) and social pressure

(3) Schweitzer Model (2006)

(4) Pintado-Watts Model (2007)

(5) Wu-Huberman (2006)


Binary Choice with Individual Adaptation

0

1 .2

-6 -4 -2 0 2 4 6

p

U1 – U2

Utility U2

Sell

Utility U1

Buy

Probability to buy: p1

•Probability to choose S1

p = 1 / (1+exp(-(U1- U2)))

•Probability to to choose S2

1-p = 1 / (1+exp(-(U2- U1)))

Binary choice model: Logit Mode

Adaptive choice to previous choice of his own and the others

P1(t+1): the probability to choose S1 at time t+1

)()1()()1( 211 tSUUtp αα −+−=+

S(t):the proportion of the agents to choose S1 at time t

10 ≤≤ α


So what’s missing?(1): Agent’s Heterogeneity

Social pressureAGENT

Social network changes an agent’s behaviour

Preference

Preference determines an agent’s behaviour

Social pressure influences an agent’s behaviour

Need to evaluate not only stability but also individual and collective welfare

(1) Preference heterogeneity(2) Social influence heterogeneity(3) Degree heterogeneity: social networks


So what’s missing? (2): Learning Agenda

How should agents learn in the context of other learners?

Learning Agent

Game theory equilibrium agenda : How simple adaptive rules lead the agents to an

equilibrium? (It is not required any optimal requirement).

Multi-agents agenda: What is the best learning algorithm?Social engineering agenda: How should agents learn to improve collective

performance?


Outline



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.


Riyo Mori

Beauty Contest as Social Choice

JapanHoney Lee

KoreaUSA Rachel Smith

Tatiana KotovaRussiaBrazil

Natalia Guimaraes

<Miss Universe 2007>


Social Choice

•There is set of alternatives to be ranked.•Each member has different preference. •The society have to decide ordering on all alternative, which is the best, the second best,and so on.

Majority voting rule “Choice A should beat B if more people prefer A to B

Binary choices ➭ No problem: elect the choice with more votes!

Social choice:Forming social

preference

Social choice:Forming social

preference

Independen preference


Paradox of VotingHow to extend the idea with more than two choices?

➭We have the problem known as “paradox of voting.”:Three candidates: {a, b, c}, Three voters : {A, B, C}

Preference ordersA: B: C:

Group choice:

α

cb ffα acb ff bac ff

acb fffαa b c

Borda index:

a:6, b:6, c:6


Consensus Formation with Individual Adaptation

Preference adaptation

Forward problem

Aggregatedpreference

Aggregatedpreference

<Inverse problem>

How should agents preferences be adapted to aggregated preference for better consensus formation?

Inverse problem

<Forward problem: social choice problem>

How individual preferences should be aggregated for social choice?


Preference Indexing and Aggregation

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

Indexing preference

54321 ,,,, ooooo


Adaptive Consensus Formation

The balance between individual preference and the aggregated preference.

α

: Aggregated preference of the choice j (bordascore)

: Preference of agent i of the choice j.

: speed of adaptation

)( jOG

)( ji OC

)()1()()( jiji OCOGOC αα α −+=Individual adaptive process:

Adaptation means:

“Concern not only individual but also group preference”

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

Preferences of five agents (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

}5,...,2,1:{ : }5,...,2,1:{ :

==

Group B: the adaptive speeds are different

Group A: Consensus was not formed

==iOWesalternativFive

iAGagentsFive

i

i

Group A: the adaptive speed is low and the same

Group B: Consensus was formed

(Scores of each alternative)

(Each score of alternatives are same. =Ordering of alternatives was fail. )

Group A: Consensus was not formed

Group B: Consensus was formed.

43215 ooooo ffffGroup consensus:


Beauty Contest as Guessing Game

R. Nagel experemented “beauty contest game” (1995).

“Human subject are asked to choose a number from [0, 100]. One who chooses a number as close to 2/3 of the average win the prize.”

: A naive agent would be to choose ranodmly, then the average is 50. : A sophisticated agent, wishing to maximize his chances of winning a prize, and if she believes that the others are naïve the average is 50, she will pick a number above 50 x 2/3.: A more sophisticated agent believes that the others are sophisticated,and then she will pick a number 100 x 2/3 x 2/3.

: If agents are so smart make a selection based on some inference from his knowledge of public perceptions, the collective inductive process converge to zero, which is the unique Nash equilibrium.


Outline



How Do Three Factors Influence on Social Dynamics?

Social pressureAGENT

Social network changes an agent’s behaviour

(1) Preference heterogeneity(2) Social influence heterogeneity(3) Degree heterogeneity

Preference

Preference determines an agent’s behaviour

Social pressure influences an agent’s behaviour


Beauty Contest Games with Externalities

“In a stock market investors care about what other investors will buy in the future.”

<Payoff scheme>

Majority game: One who picked the face of the majority choice wins a prize.”

Minority game: One who picked the face of the minority choice wins a prize.


Binary Choice Model: Logit Model

0

1 .2

-6 -4 -2 0 2 4 6

p

U1 – U2

Utility U2

Sell

Utility U1

Buy

Probability to buy: p1

•Probability to choose S1

p = 1 / (1+exp(-(U1- U2)))

•Probability to to choose S2

1-p = 1 / (1+exp(-(U2- U1)))


Beauty Contest as Majority Games

α : preference (motivation)α > 0 : agent i prefers S1

α < 0 : agent i prefers S2

β : social influence

U(S1)= βp + α

U(S2)= β(1−p)

p

U S( )1

0

U S( )2

1

Payoff

α

β

θThresholdθ =(1- α /β)/2

p : the proportion of agents who choose S1

Agents receive more payoff if more agents choose the same choice

Agent’s utility


Decision Rule: Majority Game

The payoff matrix

p 1-p

The otheragents

Agent Ai

S1

S1

S2

S2

α + β α0 β


Thresholdθ =(1- α /β)/2

Rational decision rule

p > θ → choose S1

p < θ → choose S2

U(S1)-U(S2) = 2βp + α - β

equivalently transformed payoff matrix

p 1-p

The otheragents

Agent Ai

S1

S1

S2

S2

1− θ 00 θ


Beauty Contest as Minority Game

α : preference (motivation)α > 0 : agent i prefers S1

α < 0 : agent i prefers S2

β : social influence

U(S1)= β(1−p) + α

U(S2)= βp

p

U S( )1

0

U S( )2

1

Payoff

α

β

θThresholdθ =(1- α /β)/2


Agent’s utility

α+β

Agents receive less payoffs if more agents Choose the same choice


Decision Rule: Minority Game


Rational decision rule

Thresholdθ =(1+ α /β)/2

p < θ → choose S1

p > θ → choose S2

U(S1)-U(S2) = -2βp + α + β

1− θ

equivalently transformed payoff matrix

p 1-p

The otheragents

Agent Ai

S1

S1

S2

S2

0

The payoff matrix

p 1-p

The otheragents

Agent Ai

S1

S1

S2

S2

α α +β

β 0

θ00


Summary: Beauty Contest Games

<Payoff scheme>

Majority game: Agent wins 1− θ if he chooses S1 and if the majority choose S1

Minority game: Agent wins if he chooses S2 and 1− θ if the majority choose S1

1− θ

θ

An agents bits one unit

by splitting 1− θ on S1 and θ on S2

S1

S2


< strong preference orno social influence>

S1

S1

S2

S2

1000 S1

S1

S2

S2

0100S1

S1

S2

S2

0.50.500

BA

Heterogeneity:Preference and Social Influence

A population of hard-coresA population of social atoms

< strong social influenceor no preference>


Agent Population : Threshold Distribution

preference α:uniform distribution

Threshold: θ=(1- α /β)/2

Heterogeneous preference: αSocial pressure β : constant

preference α:normal distribution

No preference α=0 hardcore of S1:α>1hardcore of S2:α<−1


Closed-Loop Social Dynamics (1)

p(t) > θi → S1

p(t) < θi → S2

<decision rule: majority game>

<decision rule: minority game>

p(t) < θi → S1

p(t) > θi → S2

Micro-Macro Loop

Social influenceinteraction

Interaction

Agent

Collective decision


Closed-Loop Social Dynamics (2)

θi < θF(θ)=Σ n (θi )/N

The distribution pattern of the threshold

θ0.2 0.4 0.6 0.8 1.00

0.2

0.3

0

0.1

θi

n(θi)/N

The Accumulated threshold

θ1.00 0.2 0.4 0.6 0.80

0.20.40.60.81.0

θi

F(θi )

F(θ )The proportion of agents with threshold less than θ

p(t) > θi → S1 : chooses A

p(t+1)=F( p(t))Social dynamics

p(t+1)=1- F( p(t))

Agent rule(Majority game)

Agent rule(Minority game)

Social dynamics

p(t) < θi → S1 : chooses A


Simulation Results(1) :Beauty Contest as Majority Game

collective decision < average payoff: efficiency>

Case3 Case4Case2Case1

All make the same choice Coexistence Split into two choices

< payoff distribution>

Case2


Simulation Results (2):Beauty Contest as Minority Games

Case3 Case4Case2Case1

Oscillations are observed between two choices

collective decision

Minority game:important for the study of fluctuation.

Split into two choices


p(t)

0 5

0.60.8

100.00.2

1.0

0.4

t 2015 A1

A2

p(t)0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

1-F(p(t))

A1

A2

n(θ )/N

0 0.2 0.4 0.6 0.8 1.00

0.2

0.3

0.1

θThe distribution pattern of the threshold

The dynamics of collective behavior

Fluctuation in Beauty Contest as Minority Game(1)

The Accumulated threshold

Weak preference or strong social influence

p(t+1)=1- F( p(t))


p(t)

0 5

0.60.8

100.00.2

1.0

0.4

t 2015

E

The distribution pattern of the threshold

The dynamics of collective behavior

θ1

θ2

θ3

θiθ4 θ5

θn-1

θj

θn-2θ6

n(θi )/N

0 0.2 0.4 0.6 0.8 1.00

0.2

0.3

0.1

θi

=Strong preference for A

Strong preference and weak social influenceA half of agents prefer A (S1) and the rest of agents prefer B (S2)

Fluctuation in Beauty Contest as Minority Game(2)

All agents split into two groups to choose A (S1) and B (S2) starting from any initial condition.

Strong preference for B


Minority Game with Inductive Reasoning

El Farol bar at Santa Fe

The number of people in the bar

Rule learning in minority game

D. Challet and Y.-C. Zhang,Physica A 246, 407 (1997)

W. B. Arthur, Amer. Econ. Review 84, 406 (1994).


Minority Games with Global Interaction

A=# of agents who attended σ

Nash equilibrium(S1: 0.5, S2: 0.5)

>−<= 2)2/( NAσ

Efficient coordinationis emergent

Number of behavioral rules

(inefficiency)Challet, Zang (2005)

random behaviorherding behavior

diversityhomogeneous

Global interaction: interact with all other agentsModerate diversity: important for emergence of coordination


Minority Game on Social Networks

the smallest volatility

S. Lee and H.Jeong ( 2005)

What if we connect the players by different

networks?

Substrate networks determines volatility


Beauty Contest as Mixed Majority and Minority Games

p(t+1) =(1-k)(1- F2( p(t)) +kF1( p(t))

k: the proportion of conformists

θn-1θ1

θ2

θ3

θl

θ4θ5 θn

θjθn-2

θ6

Social Dynamics

p(t) > θi → S1 : choose Ap(t) < θi → S2 : choose B

p(t) < θi → S1 : choose Ap(t) > θi → S2 : choose B

ConformistsNon-conformists

Conformist: Agents who play the majority gameNon-conformist: Agents who play the minority game

Collective decision of the mixed population


Simulation Results (1)

k=80%k=50%k=30%

Social atoms: identical agents with no preference

simulation results


The distribution pattern of the threshold The distribution pattern of the threshold



k=80%k=50%k=30%

Populations of heterogeneous agents





k=80%k=50%k=30%

Population of heterogeneous agents with strong preference




66

Simulation Setting: Majority GameAgent preference parameter: θ

Agent rational rule

Diversity of the populationdensity of θ: f(θ)

S1 S2

S1 0S2 0

θ−1θ

Aggregate or local information

p

5.0<θ5.0>θ

： prefer S1 ： prefer S2

θ>)(tpθ<)(tp

： choose S1 ： choose S2


68

Frangibility of Collective Decision with Hub Agents (1)

Initial proportion of S1

◆: Global model▲: Local model (4 neighbors)

proportion of S1

Two phases depending on the initial condition(1) Consensus on one opinion

(2) Coexistence different opinions0.25 < p(0) < 0.75

p(0) <0.25, p(0)>0.75

Interaction with a few neighbors promote coexistence of the different opinions

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1p(0)

p*

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1p(0)

p*

Hub ModelGlobal/Local modelproportion of S1


0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1p(0)

p

0

0.02

0.04

0.06

0.08

0.1

0 0.25 0.5 0.75 1p(0)

⊿p

0

0.02

0.04

0.06

0.08

0.1

0 0.25 0.5 0.75 1p(0)

p

Frangibility of Collective Decision with Hub Agents (2)

●: S1 ●: S2●: S1⇔S2●: S2⇔S1

Case 1: local model Case 2: hub and 4 neighborsCase 2: hub and 1 neighbor

the fluctuation of p⊿p

⊿p ⊿p

Subgroup1 Subgroup 2


Outline



Contagion and Innovation ModelsConcept of contagion arises in many fields• Spread of infectious disease• Emergence of collective beliefs• Transmission of cultural fads• Diffusion of innovations

Question 1: In what sense are these phenomena the same and how are they different?Question 2: Are individuals more influenced by their immediate partners or are they more influenced by the adoption behavior of the social system?Question 3: What conditions or behaviors trigger the decision to adopt something?


Complexity and SerendipityComplexity • The whole is greater then the sum of its parts• Global properties emerge from local interactions• Networks underlie complexity

What is Serendipity?Accidental discovery: named after

“Three Princes of Serendip”Result of complexityFortune favours the prepared mind …No serendipity unless you see itInteraction of different ideas and exploration

The Serendipity Machine

David G. GreenMonash University,Australia, 2005

Modern computing relies on serendipity

Data mining

Evolutionary computing

Computers have unexpected side effects


Spreading Better Rules(1): Problem Setting

：θ＜0.5： θ＞0.5

A

S1

S1

S2

S2

0

00

0

B

0.80.8

0.20.2

Different types: battle of sexes game

A

S1

S1

S2

S2

0

00

0

B

0.2

0.8

0.2

0.8

Same type: coordination game

A

Random location:An agents plays with different type


All Possible Rules based on the Past OutcomeType 1: 0 0 0 0 (ALL-C) Type 9: 0 0 0 1Type 2: 1 0 0 0 Type 10: 1 0 0 1Type 3: 0 1 0 0 Type 11: 0 1 0 1 (TFT)Type 4: 1 1 0 0 Type 12: 1 1 0 1Type 5: 0 0 1 0 Type 13: 0 0 1 1Type 6: 1 0 1 0 Type 14: 1 0 1 1Type 7: 0 1 1 0 (PAVLOV) Type 15: 0 1 1 1 (FRIEDMAN)Type 8: 1 1 1 0 Type 16: 1 1 1 1 (ALL-D)

Investigate which rules will spread and survive

Own Opp4 0 0 #5 0 1 #6 1 0 #7 1 1 #

strategy at tbitpast strategy

Memory of past historyFirst Owns Hand

Own Strategy

１ 62 7bit3 4 5

S1: 0S2: 1

#: 0 or 1

Random Location of Heterogeneous Agents

0.48

1

0

Type1:0000

Type2:0001

Type3:0010

・

・

・

Type15:1110

Type16:1111

average payoff

There are 24=16 possible rulesWhat rules are survived?How efficient rules spread out?

payoff matrixThe other

agentsAgent i

S1

S1

S2

S2

1− θ 00 θ


Dynamic Diffusion Process of RulesWhat rules are survived?

How efficient rules spread out?


Structured Location

：θ＜0.5： θ＞0.5

A

S1

S1

S2

S2

0

00

0

B

0.80.8

0.20.2

Same type: coordination game

A A

S1

S1

S2

S2

0

00

0

B

0.20.2

0.80.8

Segregated location:An agent play with the same type


Simulation Result: Segregated Location

Noise: 10%Noise: 0%

Two efficient rules spread out with some noise. However many rules survive without noise


Noise Promotes Diffusion of Better Rules

Innovation map at the 25th generation

Average payoff

Noise: 10%

Noise: 0%

Innovation map at the 50th generation


Exploring Better Rules: Problem Setting(1)

Memory of past historyFirst Owns Hand

Own Strategy

１ 62 7bit3 4 5

Own Opp4 0 0 #5 0 1 #6 1 0 #7 1 1 #

strategy at tbitpast strategy

The otheragents

Agent Ai

S1

S1

S2

S2

1− θ

0 θ

0

＜minority games>

Crossover


Exploring Better Rules (3)

Small-world NetworksLattice Networks Random Networks

type1 = 1,1,0,1,0 (719)type2 = 0,1,0,1,1 (380)type3 = 1,1,0,0,1 (842)type4 = 0,1,0,0,1 (559)

Learned rules:Give-and-takeTurn-taking



Learned rules: Win-stay, lose-shift

Learned rules: Win-stay, lose-shift


Outline



• Crowds are often foolish, but crowds are wise under certain conditions

-- Under what mechanism can we improve the performance of Under what mechanism can we improve the performance of collective systems of agents in a networked world?collective systems of agents in a networked world?

Social Engineering (1)


A large collection of people are smarter than an elite few. In “the Wisdom of Crowds”, 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)

Social Engineering (2)


Five Stages of Research

1) Observe: Gather data to demonstrate power law behavior in a system.

2) Interpret: Explain the import of this observation in the system context.

3) Model: Propose an underlying model for the observed behavior of the system.

4) Validate: Find data to validate (and if necessary specialize or modify) the model.

5) Control: Design ways to control and modify the underlying behavior of the system based on the model.

Focus on control issues: Lots of open research problems in the study of networked systems


Illusion of Control?

Internet throughput

self-similarities Meta-stabilities

distribution of call types inwireless cells

synchronization among routers

phase transitions

unordered equilibrium(self-organized criticality)

oscillation

chaos

turbulence

high load congestion collapse

Difficult to predict and control because of phase-transitional behavior


Incentive ControlGeneral problem: given a good social model, determine how to change social system behavior to optimize a global performance.In many social systems, intervention can impact the outcome.• Typical setting: individual agents acting in their own

best interest, giving a partial global view. • Agents can be given incentives to change behavior.• Distributed algorithmic mechanism design.• Mix of economics,game theory, computer science,

statistical physics, and complex networks.


So what’s missing?

A very large-scale computation is done by with 1023 social atoms, each equipped with nothing more than knowledge of their immediate neighbourhood and behavioural rules

How smart do agents need to be?

Nana

Social

NanaN=1023

ActionInformationgathering

Decision


Conclusion of Today’s Talk

I considered two related issues in social dynamics.

: One is the connection between individual behaviors and aggregated outcomes.

: The second is the role of social networks in determining macroscopic outcomes and dynamics.

The main issue is not how much rationality there is at the micro level, but how little is enough (selfish + sociality) to generate desirable macro-level patterns in which most agents are behaving as if they were rational.


Low

Low

High

High

Scale of problem

Multi-agentsystems

Socio physics(Complex networks)

Social Engineering

Game theory

Selfish agentSelf-interest seeking of elements

Social atom


Thank you for listening!!

The Theory of Social Interaction and Social Engineeringnama/Top/InvitedTalk/07-04_it.pdf0 -...

Documents

Transcript of The Theory of Social Interaction and Social Engineeringnama/Top/InvitedTalk/07-04_it.pdf0 -...