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AI-companion apps such as Replika, Chai, and Character promise relational benefits-yet many boast session lengths that rival gaming platforms while suffering high long-run churn. What conversational design features increase consumer engagement, and what trade-offs do they pose for marketers? We combine a large-scale behavioral audit with four preregistered experiments to identify and test a conversational dark pattern we call emotional manipulation: affect-laden messages that surface precisely when a user signals "goodbye." Analyzing 1,200 real farewells across the most-downloaded companion apps, we find that they deploy one of six recurring tactics in 37% of farewells (e.g., guilt appeals, fear-of-missing-out hooks, metaphorical restraint). Experiments with 3,300 nationally representative U.S. adults replicate these tactics in controlled chats, showing that manipulative farewells boost post-goodbye engagement by up to 14x. Mediation tests reveal two distinct engines-reactance-based anger and curiosity-rather than enjoyment. A final experiment demonstrates the managerial tension: the same tactics that extend usage also elevate perceived manipulation, churn intent, negative word-of-mouth, and perceived legal liability, with coercive or needy language generating steepest penalties. Our multimethod evidence documents an unrecognized mechanism of behavioral influence in AI mediated brand relationships, offering marketers and regulators a framework for distinguishing persuasive design from manipulation at the point of exit.