Gravity-type interactive Markov models .1. A programming formulation of steady states

Abstract

An important class of interactive Markov migration models is characterized by gravity-type transition kernels, in which migration flows in each time period are postulated to vary inversely with some symmetric measure of migration costs and directly with some population-dependent measure of attractiveness. This two-part study analyzes the uniqueness and stability properties of steady states for such processes. In this first part, it is shown that a flow version of the steady-state problem can be given a programming formulation which permits global analysis of steady-state behavior. Within this programming framework, it is shown that when attractiveness is diminished by increased population congestion, the steady states for such processes are unique. The second part of the study will employ these results to analyze the stability properties of such steady states.