Abstract
Intuition suggests that in markets with consumer lock-in (‘brand loyalty’), firms with a large customer base earn higher profits. We show for a homogeneous goods duopoly that the intuition can be misleading, as the intensity of price competition depends on the initial market split. We derive mixed-strategy equilibria, and show that competition is often most intense when the market is split evenly. As a result, firms coordinate on an asymmetric split when consumers are not yet attached to firms. We also allow for asymmetric costs, and analyze when firms with a larger customer base are more eager to innovate.
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