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Competition with asymmetric switching costs

We analyze the effects of asymmetric switching costs on two identical firms that produce an homogeneous

good and compete in prices. Both firms inherit a fraction of themarket which is “locked-in” by the switching costs. When switching costs are low, firms face a tradeoff between charging a high price to their locked in customers, or pricing aggressively in order to attract the rival’s market share. We characterize the (pure and mixed) equilibrium strategies and the associated payoffs for any pair of switching costs in the unit square.