Benoit Mahault (Universite Paris Sud; Los Alamos National Laboratory)
Abstract. Inspired by work on artificial frustrated materials, we introduce a model to describe shared wealth on a network. Ideas from trapped colloids on a lattice readily find a generalization to describe wealth distribution in the network of a society. We concentrate on the relation of wealth with a degree of freedom often absent in social studies: opportunities. We show that in a completely unconstrained situation, i.e. a purely libertarian setting where wealth is accessible to anybody who has opportunity to grab it, an ordered picture tends to extreme polarization, where an upper class of high opportunities has all of them satisfied, while a lower class sees all its opportunities unfulfilled. Disorder ameliorates the picture only partially, by creating a middle class characterized by high motivation, defined as the marginal increment of wealth with increased opportunities. The system, however, can be severely frustrated by hard constraints, when the opportunities of the agents are pairwise connected to form a network. Then the structure of the network determines the allocation of wealth vs. opportunities, often making it fairer, although not necessarily improving its equality as described e.g. by a Gini index. We discuss scale free, Erdos random networks, and as a counterexample a generalization of the Bethe graph. We suggest how these idea of dynamics on the network can be implemented to model dynamics of the network.