Diffusion of information and phase transition in the Fisher market

Abstract

In this paper, we study the effect of diffusion on the evolution of a market consisting of two infinitely divisible goods and buyers with constant elasticity of substitution utility functions. In consecutive time periods, the buyers’ preferences depend on the actions taken by their neighbours in the network. We investigate the properties of the long time states, where a market state is defined by the market equilibrium prices and goods allocation. The experimental results demonstrate that the long time states are sensitive to initial conditions and exhibit the following patterns. Homogeneous: the market prices of the two goods are equal and the buyers split equally their budget amongst the goods. Heterogeneous: the buyers’ bids on the two goods differ. Periodic: the buyers’ bids oscillate with stable oscillation width. Moreover, we present the critical values where a phase transition occurs between homogeneous, heterogeneous and periodic states.