Threshold learning dynamics in social networks


The java applet below visualizes the dynamics of a threshold model to study problems of social learning [1] . The interaction dynamics is inspired by the threshold model introduced by M. Granovetter [2].

 

References:

[1]  J.C. González-Avella, V.M. Eguíluz, M. Marsili, F. Vega-Redondo, M. San Miguel, Threshold learning dynamics in social networks, arXiv:1008.3083v1, (2010).

[2]  M. Granovetter, Threshold Models of Collective Behavior, The American journal of Sociology 83 (6), pp. 1420-1443, (1978).

 


Dynamical rules for the model:

The system consists of N agents placed at the nodes of a network. Each node is connected to k neighbors and can choose between two states, denoted by +1 and -1.

As initial condition, agents with state +1 are uniformily distributed at random with probability p in the system, while agents with state -1 are also uniformly distributed at ramdom with probabilty 1-p.

The system evolves by iterating the following time steps:

(1) An agent i is randomly chosen in the system.

(2) This agent receives an external signal E, indicating state +1 with a probability p, and state -1 with probability 1-p.

(3) If the state of the external signal is equal to that of the selected agent, nothing happens. Otherwise, agent i evalutes the states of its ki neighbors. If the fraction of neighbors agreeing with the state of the signal is greater than a threshold value τ, agent i adopts the state of the external signal. If the fraction of neighbors agreeing with the state of the signal is smaller that τ, agent i keeps its state.

 

Applet on a fully connected network.

Applet on a regular lattice



Created by J.C. Gonzalez-Avella