Competition for territories under the switching cost

Abstract

In this subsection, a two-stage game is analyzed; in the first stage, both stores declare their DAs simultaneously; then, in the second stage, stores determine their uniform price simultaneously. When there is no switching cost, the subgame Nash equilibrium in the second stage exists only if in the first stage stores choose DAs that cover most of the area, although they have incentives to shrink their DAs in the first stage. There is no subgame perfect equilibrium here.Further, when positive switching cost is assumed, the subgame perfect Nash equilibrium exists in limited cases, where the switching cost is sufficiently large. At the equilibrium, both DAs cover all the area, and the prices are increased up to the ceiling reservation price. This means no territories are established in this model, although the model aims to investigate equilibria where territories are established. A.2 Two-stage Game without Switching CostConsider Game 0 defined as: Game 0.X δ = 0.X The first stage: both stores declare their DAs simultaneously.X The second stage: stores choose their uniform price simultaneously.Except when both DAs were declared in the first stage to cover most of the market area, or when they are separated, Nash equilibrium does not exist in the second stage as is shown Lemma A1.