Spatial agglomeration or dispersion under Cournot-Bertrand competition

This research explores the equilibria of a spatial model with consumers having finite reservation prices and two firms under Cournot-Bertrand competition. We find three types of equilibria. For high effective reservation prices, a unique equilibrium exists with spatially agglomerating firms serving all consumers. For medium effective reservation prices, the intermediate-location-differentiation firms serve all consumers at equilibria. For low effective reservation prices, the firms act as two monopolists and do not serve all consumers at equilibria. The results herein and from previous studies together demonstrate that changing one of two Bertrand (Cournot) firms to Cournot-type (Bertrand-type) can make the minimum-location-differentiation equilibrium appear (disappear). Moreover, both firms' location distances at our intermediate-location-differentiation equilibria are always larger than those at the equilibria of firms' price competition.