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Understanding the Impact of Churn in Dynamic Oligopoly Markets

We incorporate the effects of churn, which refers to customers switching to competing brands, in a dynamic model of advertising for oligopoly markets. Each firm's market share depends not only on its own and competitors' advertising decisions, but also on market churn. Applying differential game theory, we derive a feedback Nash equilibrium under symmetric and asymmetric competition. We obtain explicit solutions and discover the counter-intuitive result that, as market churn increases, firms should decrease advertising rather than increase it to counteract the impact of churn.