In collaboration with V. Koulovassilopoulos, we studied the role of asymmetric interactions in the consumption behaviour of a network of heterogeneous agents. Direct interactions among economic agents, usually refer to as social interactions (as opposed to market mediated interactions) are meant to capture how the decision of each individual is influenced by the choice of others in his reference group. Direct interaction models can apply to coordination problems in general, ranging from the emergence of collective political actions and the development of fads and conventions to the explanation of speculative bubbles in financial markets and the dynamics of market penetration and diffusion of technological innovations. In the literature the attention has been mainly focused on the case of positive, pairwise symmetric, spillover, i.e. the case where the payoff of a particular action increases when others behave similarly.
We assume that the interactions among agents are uniquely specified by their “social distance” and that the consumption decision is driven by peering, distinction and aspiration effects. We analyze the problem in the framework of discrete choice models with stochastic decision rules and specified
the interactions of microeconomic units in terms of transition probabilities of Markov chains. This problem has been analyzed using the techniques of statistical mechanics. In the case of symmetric interactions, the equilibrium condition can be expressed in terms of the Boltzman distribution.
This is no more possible in models with asymmetricinteractions (the detailed balance condition does not hold), and the long time behaviour of the system has to be calculated by solving the dynamical problem. We explored the dynamical properties of the model by numerical simulations, using three different evolution algoriths with: paral lel, sequential and random-sequential updating rules. We focus on the long-time behaviour of the system which, given the asymmetric nature of
the interactions, can either converge into a fixed point or a periodic attractor.