Model of spatial competition on discrete markets

TL;DR

This paper introduces a dynamic model of price formation on spatial markets represented by graphs, analyzing how seller positions and information levels influence price stability, cycles, and competition measurement, with applications to real city street networks.

Contribution

It presents a novel dynamical model for spatial market competition, including a new measure of node centrality based on market relevance.

Findings

Prices can stabilize or cycle depending on seller positions and information levels.

The model quantifies competition strength via price scaling exponents.

Application to real city street networks reveals varying competition levels.

Abstract

We propose a dynamical model of price formation on a spatial market where sellers and buyers are placed on the nodes of a graph, and the distribution of the buyers depends on the positions and prices of the sellers. We find that, depending on the positions of the sellers and on the level of information available, the price dynamics of our model can either converge to fixed prices, or produce cycles of different amplitudes and periods. We show how to measure the strength of competition in a spatial network by extracting the exponent of the scaling of the prices with the size of the system. As an application, we characterize the different level of competition in street networks of real cities across the globe. Finally, using the model dynamics we can define a novel measure of node centrality, which quantifies the relevance of a node in a competitive market.