Patterns of consumption in a discrete choice model with asymmetric interactions

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We study the consumption behaviour of an asymmetric network of heterogeneous agents in the framework of discrete choice models with stochastic decision rules. We assume that the interactions among agents are uniquely specified by their ``social distance'' and consumption is driven by peering, distinction and aspiration effects. The utility of each agent is positively or negatively affected by the choices of other agents and consumption is driven by peering, imitation and distinction effects. The dynamical properties of the model are explored, by numerical simulations, using three different evolution algorithms with: parallel, sequential and random-sequential updating rules. We analyze 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. We discuss the role of symmetric versus asymmetric contributions to the utility function and also that of idiosyncratic preferences, costs and memory in the consumption decision of the agents.