A spatial Herfindahl–Hirschman Index for inter- and intra-type competition

We propose a density-aware spatial extension of the Herfindahl–Hirschman Index (sHHI) that incorporates population distribution and facility locations into measures of market concentration. The approach uses Voronoi catchments to allocate population to the nearest unit and derives concentration measures at both unit and type levels. We further introduce a nested decomposition that distinguishes inter-type competition from intra-type crowding. Using simulations, we examine the behaviour of the index under alternative spatial configurations of demand and supply. Empirical illustrations for Warsaw retail networks and public schools demonstrate how accounting for spatial heterogeneity alters concentration assessment and supports location-allocation decisions.