Working Paper BETA #2023-33

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Title : Spatial multiproduct competition

Author(s) : Moez Kilani, André de Palma

Abstract : We analyze spatial competition on a circle between firms that have multiple outlets and face quadratic transport costs. The equilibrium is a two-stage Nash game: first, firms decide on their locations and then set their prices. We are able to solve analytically simple multi-outlet cases, but for the general case, we require an algorithm to enumerate all non-isomorphic configurations. While price equilibria are explicit and unique, solving the full two-stage game requires numerical methods. In the location game, we consider two scenarios: either firms cannot jump one outlet over a competitors’ outlet, or firms have the flexibility to locate outlets anywhere on the circle. The solution involves a balance between cannibalization, market protection, and spatial monopoly power. We compare prices, profits, and transport costs for all possible configurations. With flexible locations, the firms’ market areas are contiguous. In this case, surprisingly, each firm acts as a spatial monopoly. If regulations enforce that each firm must set the same price for its outlets, head-to-head competition prevails, leading to decreased profits for the firms but to a better-off situation for consumers.

Key-words : Spatial competition, circle, multi-product oligopoly, price-location equilibria, coin change problem.

JEL Classification : L13, R32, R53