Spatial competition and price formation

Abstract

We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for information transmission, that is, consumers can only learn from nearest neighbors. Many aspects of this can be understood in terms of generalized evolutionary dynamics. In consequence, we first look at spatial competition and cluster formation without price. This leads to establishement size distributions, which we compare to reality. After some theoretical considerations, which at least heuristically explain our simulation results, we finally return to price formation, where we demonstrate that our simple model with nearly no organized planning or rationality on the part of any of the agents indeed leads to an economically plausible price.