Discrete Choice via Sequential Search

Essentially every choice involves an information collection or search phase prior to a decision-making phase that culminates in a choice. To study the information collection phase within an important class of search problems and understand how it influences the final choice, we embed an analytically tractable discrete choice model in a classical model of sequential search with perfect recall. Although significant progress has been made in the theory literature in analyzing consumers’ discrete choice behavior using random utility models, discrete choice through a sequential search process has not received enough attention at least in part because of analytical intractability issues. We build on the seminal Pandora’s Problem as a model of sequential search with perfect recall and on Exponomial Choice as a model of discrete choice (with each choice specified by a deterministic or observable utility component minus a random or unobservable utility component following an exponential distribution). We derive the search path and final choice probabilities in closed form, develop all the analytical tools to optimize prices for a given assortment of products, and show that the optimal assortment must contain some number of highest-value products at optimal prices. These results enable joint optimization of assortment and prices efficiently. The structure of the solution features a distinct group of products that are priced just so they remain on the search path with higher probability. Through simulation studies, allowing us to control the ground truth, we also show that our model is competitive against the state of the art in empirical modeling of sequential search and that ignoring sequential search distorts both optimal variety and pricing decisions in an upward direction. This paper was accepted by Omar Besbes, revenue management and market analytics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.01552 .