Competitive multi-facility location games with non-identical firms and convex traffic congestion costs

This paper studies a set of heterogenous competitive firms simultaneously locating facilities at a set of locations to serve a set of markets. Firms incur firm-specific transportation, congestion, and location costs, and market price is linear and decreasing in the amount shipped to the market by all firms. First, firms’ market-supply decisions for given facility locations are characterized using a variational inequality formulation. Then, firms’ location decisions are analyzed. A heuristic method is provided for finding equilibrium locations, and its computational efficiency is compared to a random search method.