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The Theory of Social Interaction and Social Engineering

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The Theory of Social Interaction and Social Engineering 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 • me-varyingunication topology might be timCom The distributed consensus algorithm x( t 1i+ ) x = ( ti )ε +∑ wij ( j x (− t)i x ( t )) i∈ Ni The weighted adjacency matrix G=(wij) (i) raph G is connectedG (ii) G is balanced: w= w ∑i≠ j ij ∑j≠ i ji Convergence to the average of the initial values of all agents x=1 x = 2 ... = xn =(i 0 x ) / n ∑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 j i 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 = <k> disease dies c <k2> disease spreads <k>: 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 { 0 ,− 1⎤ } ⎢ k ⎥ ⎢ 2 ⎥ ⎢ ⎥ λ2 = 0.238 λ2 = 0.925 O ⎢ ⎥ {⎣ 0 ,− 1 } 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
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