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Understanding the impact of churn in dynamic oligopoly markets. (English) Zbl 1252.93013

Summary: 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.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
91G10 Portfolio theory
49N70 Differential games and control
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References:

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