Spin-glass-like Dynamics of Social Networks

In this work we study spin-glass (SG) like behavior in the dynamics of multiple agents in a social or economic context using interactions which are similar to the physical case. The different preferences shown by individual agents are represented by orientations of spin-like variables. Because of limited resources, each agent tries to maximize her total utility function, giving a prescription for the dynamics of the system similar to the evolution resulting from the optimization of the interaction of a SG. The coupling between agents for different attributes may be positive or negative, as in a physical SG system, forming "frustrations" from the ensuing conflicts, with the system trying to find an overall equilibrium, but in vain, so that we observe oscillations. The couplings are provided by matrices corresponding to each attribute and each agent, which are allowed to have some fixed bias, indicating the unchangeable component of the make up of the agents from genetic factors or lasting environmental influences, and also contain a random part from environmental noise, i.e. the cumulative stochastic effect of lumped factors not explicitly accounted for in the model.