Search with Interdependent Values

We propose a sequential search theory where values of different items are interdependent via a common attribute. Compared to the model with independent values, search here not only reveals the value of the current item, but also provides information on uninspected ones. This interdependence leads to a "cockroach" effect, that is, a bad realization can signal poor values for other items. Therefore, the agent will stop searching when the current realization is either good enough, which aligns with the literature, or bad enough, which is new to the search literature. The cockroach effect also adds up to the trade-off in determining the optimal search order, making small-variance items valuable as they contain more information on the common attribute. Finally, our theory predicts recall behavior as well as history-dependent search order, which further complements the existing search theory