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) Scale of problem Related Disciplines

High Socio physics Agents in a (Complex networks) connected world

Multi-agent systems

Game theory

Low Low High Social atom Self-interest seeking Selfish agent 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) 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) 4 - ABM-S4-ESHIA ‘07 (Agelonde, France) Dynamics of Social Atoms

Universal social phenomena No individual People follow the herd preference : Fashions Social : Panic in emergencies Social atom influence If one does it, others follow Social pressures influence agent’s behaviour Why? : 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 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. Convergence of the states of all agents to a common value

xi = xj = …= xconsensus

[01]: Olfati-Saber 2007

Source: Olfati-Saber 2007 [C1] 7 - ABM-S4-ESHIA ‘07 (Agelonde, France) Consensus on Dynamic Complex Networks

Dynamic Network of “agents” • Entities may be mobile • Communication topology might be time-varying The distributed consensus algorithm

i i +=+ ε ∑ jij − i txtxwtxtx ))()(()()1( ∈Ni i

The weighted adjacency matrix G=(wij) (i) Graph G is connected (ii) G is balanced: = ww ∑ ≠ ji ij ∑ ≠ij ji Convergence to the average of the initial values of all agents

21 ... n ==== i /)0( nxxxx ∑i 8 - ABM-S4-ESHIA ‘07 (Agelonde, France) Consensus under Partial Control

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

2 1 3

7 9 External 8 control Consensus formation with partial control 4

6 5

Consensus formation

9 - 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

10 - ABM-S4-ESHIA ‘07 (Agelonde, France) Contagion Models

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

SIλβR

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

11 - ABM-S4-ESHIA ‘07 (Agelonde, France) Universal Property of Contagion Models

•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 β •Infected agents are removed at rate γ •There is a threshold above which the •diseases spread through the population β = λ γ c

Critical mass: threshold property in social dynamics λc •The network topology affects critical mass 12 - ABM-S4-ESHIA ‘07 (Agelonde, France) Consensus Herd, Cascade on Social Networks

¾ 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…

¾ 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.

13 - ABM-S4-ESHIA ‘07 (Agelonde, France) Example: Underlying Network Topology Influences Critical Mass

The critical mass is given at Random & SW networks ρ λ = disease dies c disease spreads

: average degree of node λ c λ

Scale-free networks

Scale-free network does not have critical mass

14 - ABM-S4-ESHIA ‘07 (Agelonde, France) Time to Reach Consensus: Voter Model nA:proportion of A SW network Intuitive: the time to reach complete ordering is smaller 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, regular lattice more disordered, and orders rapidly only at the very end

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

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

15 - ABM-S4-ESHIA ‘07 (Agelonde, France) ConsensusConsensus andand SynchronizationSynchronization “Consensus has connections to problem in synchronization”

“Emergent behavior on flocks”

16 - ABM-S4-ESHIA ‘07 (Agelonde, France) Vicsek T,.Phys Rev Letter (1995) SynchronizationSynchronization inin GloballyGlobally ConnectedConnected NetworksNetworks

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)

17 - ABM-S4-ESHIA ‘07 (Agelonde, France) SynchronizationSynchronization inin LocallyLocally ConnectedConnected NetworksNetworks

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)

18 - ABM-S4-ESHIA ‘07 (Agelonde, France) SynchronizationSynchronization in Small-World Networks

Start from a nearest neighbor G. Ron Chen (2006) coupled network small-world network Add a link, with probability p, between a pair of nodes

Good news: A small-world network is easy to synchronize!!

X.F.Wang and G.R.Chen: Int. J. Bifurcation & Chaos (2001) 19 - ABM-S4-ESHIA ‘07 (Agelonde, France) Synchronization: Underlying Network Topology

Connectivity of networks does matter for synchronization Network B Laplacian matrix Network A

⎡ k1 − }1,0{ ⎤ ⎢ k ⎥ ⎢ 2 ⎥ ⎢ ⎥ λ2 = 0.238 λ2 = 0.925 O ⎢ ⎥ ⎣ − }1,0{ kn ⎦ Laplacian matrix = Degree – Adjacency matrix

λ1 = 0 is always an eigenvalue of a Laplacian matrix

λN/ λ２：algebraic connectivity is a good measure of synchronization. Fiedler, “Algebraic connectivity of graphs,”

Czechoslovak Mathematical Journal, 1973, 23: 298-30520 - ABM-S4-ESHIA ‘07 (Agelonde, France) Summary: Dynamics of Social Atoms

No individual preference

Social atom Social influence

Main Issues Discussed

Critical mass phenomena

How is critical mass affected?

Coexistence of different opinions

Time to reach consensus

21 - ABM-S4-ESHIA ‘07 (Agelonde, France) Collective Decision: Naive Assumption

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

For binary choice voting:

i)Individual agents: S = 0 or 1 NO YES ii)Collective decision: M = Σ S iii)Result: should be normal distribution.

0 % Collective Decision M 100%

22 - ABM-S4-ESHIA ‘07 (Agelonde, France) The Problem of Collective Decision(1)

Emergence in the collective decision process Example: Movie rankings according to votes by IMDB users. Sitabhra Sinha (2005)

Two-peaks Long-tail

In a society of agents free to choose, but they are constrained by limited information and having heterogeneous beliefs. 23 - ABM-S4-ESHIA ‘07 (Agelonde, France) The Problem of Collective Decision(2)

F. Schweitzer (2006)

24 - ABM-S4-ESHIA ‘07 (Agelonde, France) Interaction among Agents

Modeling 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) 25 - ABM-S4-ESHIA ‘07 (Agelonde, France) Binary Choice with Individual Adaptation

Buy Sell Binary choice model: Logit Mode

p1.2

Utility U2 Utility U1

•Probability to choose S1

p = 1 / (1+exp(-(U1-U2))) 0 •Probability to to choose S2 -6 -4 -2 0 2 4 6 U1 –U2

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

Adaptive choice to previous choice of his own and the others

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

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

Probability to buy: p p1(t +1) = α(U1 −U 2 ) + (1−α)S(t) 1 0 ≤ α ≤1 26 - ABM-S4-ESHIA ‘07 (Agelonde, France) So what’s missing?(1): Agent’s Heterogeneity

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

Social AGENT Preference pressure Preference determines Social pressure influences an agent’s behaviour an agent’s behaviour

Social network changes an agent’s behaviour

Need to evaluate not only stability but also individual and collective welfare 27 - ABM-S4-ESHIA ‘07 (Agelonde, France) So what’s missing? (2): Learning Agenda

9 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 collective28 - ABM-S4-ESHIA ‘07 (Agelonde, France) performance? Outline

29 - ABM-S4-ESHIA ‘07 (Agelonde, France) 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.

30 - ABM-S4-ESHIA ‘07 (Agelonde, France) Beauty Contest as Social Choice

Honey Lee Riyo Mori USA Rachel Smith Korea Japan

Natalia Guimaraes Tatiana Kotova Brazil Russia

31 - ABM-S4-ESHIA ‘07 (Agelonde, France) Social Choice

•There is set of alternatives to be ranked. SocialSocial choice: choice: •Each member has different preference. FormingForming social social preference •The society have to decide ordering on all alternative, preference 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!

Independen preference

32 - ABM-S4-ESHIA ‘07 (Agelonde, France) Paradox of Voting

How 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 orders A: α ff cb B: ff acb C: ff bac Group choice: α fff acb a b c

Borda index: α a:6, b:6, c:6

33 - ABM-S4-ESHIA ‘07 (Agelonde, France) Consensus Formation with Individual Adaptation

How individual preferences should be AggregatedAggregated aggregated for social choice? preferencepreference

Inverse problem Forward problem How should agents preferences be adapted to aggregated preference for better consensus formation? Preference adaptation

34 - ABM-S4-ESHIA ‘07 (Agelonde, France) Preference Indexing and Aggregation

Each agent has an ordered list of alternatives Indexing preference 10000

O 1 Compute the rank of the alternative 11000 10100 O 2 O 3 11010 O 11001 Rank order the alternative according to the decreasing O 4 5 sum of their ranks ,,,, ooooo 54321 Group preference preference

O α

O β

C 1 C n C 2

Oα is preferred to Oβ. n n i)( i)( OC α ∑∑ OC β )()( if i=1 < i=1 OOthen n n f βα 35 - ABM-S4-ESHIA ‘07 (Agelonde, France) Adaptive Consensus Formation

Adaptation means: “Concern not only individual but also group preference”

Individual adaptive process:

ji α OGOC α −+= α OC ji )()1()()(

OG j )( : Aggregated preference of the choice j (borda score) OC ji )( : Preference of agent i of the choice j. α : speed of adaptation The balance between individual preference and the aggregated preference. 36 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Setting

}5,...,2,1:{ : = i iAGagentsFive = }5,...,2,1:{

Five : i iOWesalternativ == }5,...,2,1:{ Preferences of five agents (Paradox of voting occurs)

Agen t 1 Agen t 2 Agen t 3 Agen t 4 Agen t 5 1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4

Group A: the adaptive speed is low and the same Group B: the adaptive speeds are different

α of Agent α of Agent Initial group derived group preference Agent1:0.1 Agent1:0.9 preference 1 2 3 4 5 5 Agent2:0.1 Agent2:0.7 1 Agent3:0.5 Agent3:0.1 1 2 3 4 5 2 derived group Agent4:0.3 Agent4:0.1 preference In itial group 3 Agent5:0.1 preference 4 Agent5:0.1 1 2 3 4 5

Group A: Consensus was not formed Group B: Consensus was formed Group A: Consensus was not formed (Scores of each alternative)

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

Group B: Consensus was formed.

Group consensus: ffff ooooo 43215 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. 39 - ABM-S4-ESHIA ‘07 (Agelonde, France) 40 - ABM-S4-ESHIA ‘07 (Agelonde, France) Outline

41 - ABM-S4-ESHIA ‘07 (Agelonde, France) How Do Three Factors Influence on Social Dynamics?

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

Social AGENT Preference pressure Preference determines Social pressure influences an agent’s behaviour an agent’s behaviour

Social network changes an agent’s behaviour

42 - ABM-S4-ESHIA ‘07 (Agelonde, France) Beauty Contest Games with Externalities

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

43 - ABM-S4-ESHIA ‘07 (Agelonde, France) Binary Choice Model: Logit Model

•Probability to choose S1

p = 1 / (1+exp(-(U1-U2))) •Probability to to choose S2

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

Buy Sell p1.2

Utility U1 Utility U2

0 -6 -4 Probability-2 0to buy2: p 4 6 1 U1 –U2 44 - ABM-S4-ESHIA ‘07 (Agelonde, France) Beauty Contest as Majority Games

Agent’s utility α : preference (motivation) α > 0 : agent prefers S U(S1)= βp+ α i 1 α < 0 : agent i prefers S U(S )= β(1−p) 2 Payoff 2 β : social influence

p : the proportion of agents who choose S1

β US()2 US()1

Agents receive more payoff if more agents choose the same choice

α 0 θ 1 p Threshold θ =(1- α /β)/2 45 - ABM-S4-ESHIA ‘07 (Agelonde, France) Decision Rule: Majority Game

The payoff matrix U(S1)-U(S2) = 2βp + α - β The other agents S1 S2 Rational decision rule Agent Ai p 1-p

p > θ → choose S1 S1 α + β α S2 0 β p < θ → choose S2 p : the proportion of agents who choose S1 equivalently transformed payoff matrix The other agents S1 S2 Agent Ai p 1-p Threshold θ θ =(1- α /β)/2 S1 1− 0 S2 0 θ

46 - ABM-S4-ESHIA ‘07 (Agelonde, France) Beauty Contest as Minority Game

Agent’s utility α : preference (motivation)

α > 0 : agent i prefers S1 U(S1)= β(1−p) + α α < 0 : agent i prefers S2 U(S )= βp Payoff 2 β : social influence

p : the proportion of agents who choose S1 US() α+β 1 US()2 β Agents receive less payoffs if more agents Choose the same choice α

0 θ 1 p Threshold θ =(1- α /β)/2 47 - ABM-S4-ESHIA ‘07 (Agelonde, France) Decision Rule: Minority Game

The payoff matrix U(S1)-U(S2) = -2βp + α + β The other agents S1 S2 Rational decision rule Agent Ai p 1-p

p < θ → choose S1 S1 α α +β

S2 β 0 p > θ → choose S2 equivalently transformed payoff matrix p : the proportion of agents who choose S 1 The other agents S1 S2 Threshold Agent Ai p 1-p θ θ =(1+ α /β)/2 S1 0 0 S2 1− θ 0

48 - ABM-S4-ESHIA ‘07 (Agelonde, France) Summary: Beauty Contest Games

S1 1− θ

An agents bits one unit by splitting 1− θ on S1 and θ on S2 θ S2

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

49 - ABM-S4-ESHIA ‘07 (Agelonde, France) Heterogeneity: Preference and Social Influence A B

A population of social atoms A population of hard-cores

< strong social influence or no preference> < strong preference or no social influence>

S1 S2 S1 S2 S1 S2 S1 0.5 0 S 1 0 S1 0 0 S2 0 0.5 1 S2 00 S2 10

50 - ABM-S4-ESHIA ‘07 (Agelonde, France) Agent Population : Threshold Distribution

Threshold: θ=(1- α /β)/2 Heterogeneous preference: α Social pressure β : constant

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

51 - ABM-S4-ESHIA ‘07 (Agelonde, France) Closed-Loop Social Dynamics (1)

Collective decision

p(t) > θi → S1 Micro-Macro Loop p(t) < θi → S2 Social influence interaction

Agent p(t) < θi → S1 Interaction p(t) > θi → S2

52 - ABM-S4-ESHIA ‘07 (Agelonde, France) Closed-Loop Social Dynamics (2)

The distribution pattern of the threshold The Accumulated threshold 1.0 F(θ)=Σ n (θ )/N 0.3 θ < θ i F(θ ) 0.8 i 0.2 0.6 n(θi)/N F(θi ) The proportion of agents 0.1 0.4 0.2 with threshold less than θ 0 0 0.2 0.4 0.6 0.8 1.0 0 0 0.2 0.4 0.6 0.8 1.0 θi θi θ θ

Agent rule p(t) > θi → S1 : chooses A (Majority game) Social dynamics p(t+1)=F( p(t))

Agent rule p(t) < θi → S1 : chooses A (Minority game) p(t+1)=1- F( p(t)) Social dynamics 53 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Results(1) : Beauty Contest as Majority Game collective decision < average payoff: efficiency> < payoff distribution>

Case2

Case1 Case2 Case3 Case4

Split into two choices All make the same choice Coexistence 54 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Results (2): Beauty Contest as Minority Games collective decision Minority game: important for the study of fluctuation.

Case1 Case2 Case3 Case4

Oscillations are observed between two choices Split into two choices 55 - ABM-S4-ESHIA ‘07 (Agelonde, France) Fluctuation in Beauty Contest as Minority Game(1)

Weak preference or strong social influence A1 1.0

0.3 0.8

0.2 0.6 1-F(p(t)) n(θ )/N 0.4 0.1 0.2 A 0 2 0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4θ 0.6 0.8 1.0 p(t) The distribution pattern of the threshold The Accumulated threshold

1.0 A2 0.8 0.6 p(t+1)=1- F( p(t)) p(t)0.4 0.2 0.0 A1 56 - ABM-S4-ESHIA ‘07 (Agelonde, France) 0510 t 2015 The dynamics of collective behavior Fluctuation in Beauty Contest as Minority Game(2) Strong preference and weak social influence

A half of agents prefer A (S1) and the rest of agents prefer B (S2)

0.3 θ1 θ θ6 θ3 n-2 θ = n-1 θ 0.2 i θ2 θj θ 4 θ5 n(θ )/N i Strong preference for B 0.1 Strong preference for A

0 0 0.2 0.4 0.6 0.8 1.0 θi The distribution pattern of the threshold 1.0 All agents split into two groups to 0.8 choose A (S ) and B (S ) starting from 0.6 1 2 E any initial condition. p(t)0.4 0.2 0.00510 2015 t 57 - ABM-S4-ESHIA ‘07 (Agelonde, France) The dynamics of collective behavior Minority Game with Inductive Reasoning

Rule learning in minority game

El Farol bar at Santa Fe D. Challet and Y.-C. Zhang, Physica A 246, 407 (1997)

The number of people in the bar W. B. Arthur, Amer. Econ. Review 84, 406 (1994). 58 - ABM-S4-ESHIA ‘07 (Agelonde, France) Minority Games with Global Interaction Global interaction: interact with all other agents Moderate diversity: important for emergence of coordination

(inefficiency)

σ = < (A − N / 2)2 > Challet, Zang (2005) A=# of agents who attended σ

herding behavior random behavior Nash equilibrium (S1: 0.5, S2: 0.5)

Number of behavioral rules homogeneous diversity Efficient coordination is emergent 59 - ABM-S4-ESHIA ‘07 (Agelonde, France) Minority Game on Social Networks

What if we connect the players by different networks?

the smallest volatility

S. Lee and H.Jeong ( 2005) Substrate networks determines volatility 60 - ABM-S4-ESHIA ‘07 (Agelonde, France) Beauty Contest as Mixed Majority and Minority Games

Collective decision of the mixed population θ1 θ θ 6 3 θn-2 θn-1 θj θl θ2 θ θ5 θn Conformist: Agents who play the majority game 4 Non-conformist: Agents who play the minority game

Non-conformists Conformists

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

k: the proportion of conformists Social Dynamics

p(t+1) =(1-k)(1- F2( p(t)) +kF1( p(t)) 61 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Results (1)

Social atoms: identical agents with no preference Non-conformists Conformists

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

k=30% k=50% k=80% 62 - ABM-S4-ESHIA ‘07 (Agelonde, France) simulation results Simulation Results (2)

Populations of heterogeneous agents

Non-conformists Conformists

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

k=30% k=50% k=80% 63 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Results (3)

Population of heterogeneous agents with strong preference

Non-conformists Conformists

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

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

64 - ABM-S4-ESHIA ‘07 (Agelonde, France) 65 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Setting: Majority Game

Agent preference parameter: θ S1 S2 ： prefer S θ < 5.0 1 S 1−θ 0 θ > 5.0 ： prefer S 1 2 S 0 θ Agent rational rule 2 tp )( > θ ： choose S1 tp )( < θ ： choose S2 Aggregate or local Diversity of the population information p density of θ:f(θ)

66 - ABM-S4-ESHIA ‘07 (Agelonde, France) 66 67 - ABM-S4-ESHIA ‘07 (Agelonde, France) Frangibility of Collective Decision with Hub Agents (1) proportion of S 1 Global/Local model Hub Model 1 proportion of S1 1

0.75 0.75 p* 0.5 ◆: Global model p* 0.5 ▲: Local model (4 neighbors) 0.25 0.25

0 0 0.25 0.5 0.75 1 0 p(0) Initial proportion of S1 0 0.25 0.5 0.75 1 Two phases depending on the initial condition p(0) (1) Consensus on one opinion p(0) <0.25, p(0)>0.75 (2) Coexistence different opinions 0.25 < p(0) < 0.75 Interaction with a few neighbors promote coexistence of the different opinions 68 - ABM-S4-ESHIA ‘07 (Agelonde, France) 68 Frangibility of Collective Decision with Hub Agents (2)

⊿p the fluctuation of p 0.1 0.1 1

0.08 0.08 0.75 0.06 0.06 ⊿p ⊿p p ⊿pp 0.5 0.04 0.04

0.25 0.02 0.02

0 0 0 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 p(0) p(0) p(0) Case 1: local model Case 2: hub and 1 neighbor Case 2: hub and 4 neighbors

●: S1 ●: S2 ●: S1⇔S2 ●: S2⇔S1

Subgroup1 Subgroup 2 69 - ABM-S4-ESHIA ‘07 (Agelonde, France) Outline

70 - ABM-S4-ESHIA ‘07 (Agelonde, France) Contagion and Innovation Models

Concept 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?

71 - ABM-S4-ESHIA ‘07 (Agelonde, France) Complexity and Serendipity

Complexity • 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 complexity Fortune favours the prepared mind … No serendipity unless you see it Interaction of different ideas and exploration

72 - ABM-S4-ESHIA ‘07 (Agelonde, France) The Serendipity Machine Modern computing relies on serendipity

ÆData mining

ÆEvolutionary computing

ÆComputers have unexpected side effects

David G. Green Monash University,Australia, 2005 Spreading Better Rules(1): Problem Setting

B Random location S S A 1 2 :An agents plays with different type 0.2 0 S 1 0.8 0 0 0.8 S2 ：θ＜0.5 0 0.2 ： θ＞0.5 Different types: battle of sexes game

B S S A 1 2 A 0.8 0 S 1 0.8 0 0 0.2 S 2 0 0.2 Same type: coordination game 74 - ABM-S4-ESHIA ‘07 (Agelonde, France) All Possible Rules based on the Past Outcome

Type 1: 0 0 0 0 (ALL-C) Type 9: 0 0 0 1 Type 2: 1 0 0 0 Type 10: 1 0 0 1 Type 3: 0 1 0 0 Type 11: 0 1 0 1 (TFT) Type 4: 1 1 0 0 Type 12: 1 1 0 1 Type 5: 0 0 1 0 Type 13: 0 0 1 1 Type 6: 1 0 1 0 Type 14: 1 0 1 1 Type 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 past strategy １ 2 34 5 6 7bit bit strategy at t

Own Opp 400 # First Owns Hand 501 # Memory of past history S1: 0 610 # Own Strategy 711 #S2: 1 #: 0 or 1 75 - ABM-S4-ESHIA ‘07 (Agelonde, France) Random Location of Heterogeneous Agents Type1:0000 Type2:0001 Type3:0010 payoff matrix ・ The other agents S1 S2 ・ Agent i ・ S 1− θ 0 Type15:1110 1 Type16:1111 S2 0 θ

average payoff 0.48

There are 24=16 possible rules What rules are survived? How efficient rules spread out? 0 Dynamic Diffusion Process of Rules What rules are survived? How efficient rules spread out?

77 - ABM-S4-ESHIA ‘07 (Agelonde, France) Structured Location

Segregated location B :An agent play with the same type S S A 1 2 0.8 0 S 1 0.8 0 0 0.2 S ：θ＜0.5 2 0 0.2 ： θ＞0.5 Same type: coordination game

B A S S A 1 2 0.2 0 S 1 0.2 0 0 0.8 S 2 0 0.8 78 - ABM-S4-ESHIA ‘07 (Agelonde, France) Simulation Result: Segregated Location

Noise: 0% Noise: 10%

Two efficient rules spread out with some noise. However many rules survive without noise 79 - ABM-S4-ESHIA ‘07 (Agelonde, France) Noise Promotes Diffusion of Better Rules

th Innovation map at the 25 generation Innovation map at the 50th generation

Average payoff

Noise: 0% Noise: 10%

80 - ABM-S4-ESHIA ‘07 (Agelonde, France) Exploring Better Rules: Problem Setting(1) ＜minority games> １ 2 345 6 7bit The other agents S1 S2

Agent Ai First Owns Hand S1 0 θ Memory of past history S2 1− θ 0 Own Strategy

past strategy bit strategy at t

Own Opp Crossover 400 # 501 # 610 # 711 #

81 - ABM-S4-ESHIA ‘07 (Agelonde, France) 82 - ABM-S4-ESHIA ‘07 (Agelonde, France) Exploring Better Rules (3)

Lattice Networks Small-world Networks Random Networks

type1 = 1,1,0,1,0 (719) type1 = 1,0,1,1,1 (2036) type1 = 1,0,1,1,1 (1695) type2 = 0,1,0,1,1 (380) type2 = 1,0,1,0,1 (441) type2 = 1,0,1,0,1 (431) type3 = 1,1,0,0,1 (842) type3 = 0,0,1,1,1 (15) type3 = 0,0,1,1,1 (321) type4 = 0,1,0,0,1 (559) type4 = 0,0,1,0,1 (8) type4 = 0,0,1,0,1 (53) Learned rules: Learned rules: Learned rules: Give-and-take Win-stay, lose-shift Win-stay, lose-shift Turn-taking 83 - ABM-S4-ESHIA ‘07 (Agelonde, France) Outline

84 - ABM-S4-ESHIA ‘07 (Agelonde, France) Social Engineering (1)

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

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

85 - ABM-S4-ESHIA ‘07 (Agelonde, France) Social Engineering (2) 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)

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

87 - ABM-S4-ESHIA ‘07 (Agelonde, France) Illusion of Control?

self-similarities phase transitions Meta-stabilities

Internet synchronization distribution of throughput among routers call types in wireless cells turbulence

unordered equilibrium chaos (self-organized criticality) Difficult to predict and control because oscillation of phase-transitional behavior

high load congestion collapse 88 - ABM-S4-ESHIA ‘07 (Agelonde, France) Incentive Control

General 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.

89 - ABM-S4-ESHIA ‘07 (Agelonde, France) So what’s missing?

How smart do agents need to be? 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

N=1023 Nana Decision

Nana Information Action gathering Social

90 - ABM-S4-ESHIA ‘07 (Agelonde, France) 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.

91 - ABM-S4-ESHIA ‘07 (Agelonde, France) Scale of problem

High Socio physics Social Engineering (Complex networks)

Multi-agent systems

Game theory

Low Low High Social atom Self-interest seeking Selfish agent of elements 92 - ABM-S4-ESHIA ‘07 (Agelonde, France) Thank you for listening!!

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