State Dependence in the “Secretary Problem”

This project develops a theoretical foundation for the search-and-consumption process underlying real-time sequential consumption. I extend the classic secretary problem along two dimensions that match the streaming environment: recursive stopping, where the agent re-enters the search process after each consumption episode rather than stopping once, and non-recall, where previously skipped options cannot be revisited. The model captures consumption on platforms like music and short-video services, where users sequentially evaluate options, consume the ones they select, and continue searching afterward — never returning to what they skipped. Because the agent re-enters search after each episode, the outcome of one consumption decision becomes part of the state governing the next: the reservation threshold is no longer constant but evolves with what was just consumed. This makes state dependence endogenous to the search process — positive when prior consumption raises the continuation value of similar options (loyalty, inertia), negative when it depresses the marginal value of the next (satiation, variety-seeking). The framework thus shows how consumers allocate attention across a stream of experiential options, generates testable predictions about how stopping behavior shifts with content-quality dispersion, consumption cost, and expectations about future options, and offers a behavioral micro-foundation for the state dependence that discrete-choice models estimate but do not explain.

Recommended citation: Yuan, Lisha and Nader Tavassoli. "State Dependence in the Secretary Problem." Research in Progress.