A Ranking Representation of Optimal Sequential Search

TL;DR

This paper introduces a ranking-based representation of optimal sequential search, simplifying implementation and extending applicability to complex search settings, thereby improving efficiency and flexibility.

Contribution

It establishes a theoretical equivalence between optimal search and ranking representations, enabling a unified and efficient empirical approach for diverse sequential search models.

Findings

Reduces simulation requirements for the classic model

Improves accuracy and computational efficiency

Extends to complex search settings like partial observations

Abstract

Sequential search models provide a powerful framework for studying consumer search using rich data that records the sequence of consumer actions taken during the search process. In existing empirical applications, their implementation often builds on optimal policies, in which later decisions depend on outcomes from earlier actions that are often fully observed by researchers. Therefore, implementation is largely restricted by computation burden and limited model flexibility. This paper establishes a theoretical equivalence showing that, under common and mild assumptions of Independence and Invariance, a sequential search process is optimal if and only if a corresponding ranking over all feasible actions throughout the process holds, thereby introducing a ranking representation of optimal sequential search. This representation enables a novel, simple, and unified empirical strategy for implementing sequential search models. For the classic \cite{weitzman1979optimal} model, the proposed approach reduces simulation requirements while improving accuracy, computational efficiency, and ease of implementation. We further show that the same strategy extends to a broad class of sequential search settings, including partially observed action sequences and multi-stage information acquisition, such as discovery. Overall, the results enhance both the tractability and the empirical applicability of sequential search models.