Title: Diffusion of information and phase transition in the Fisher market

Authors: Nikos Salamanos; Michalis Vazirgiannis

Addresses: Department of Informatics, Athens University of Economics and Business, 76, Patission Str., GR 10434 Athens, Greece ' Department of Informatics, Athens University of Economics and Business, 76, Patission Str., GR 10434 Athens, Greece

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.

Keywords: information diffusion; cascading behaviour; Fisher market; social networks; phase transition; dynamic systems; buyer preferences; homogeneous state; heterogeneous state; periodic state; market states; market equilibrium prices; goods allocation.

DOI: 10.1504/IJKL.2012.051678

International Journal of Knowledge and Learning, 2012 Vol.8 No.3/4, pp.259 - 281

Received: 10 Apr 2012
Accepted: 17 Sep 2012
Published online: 04 Sep 2014 *

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