Nested search
Yutong Zhang
TL;DR
The paper introduces a nested search model on a rooted tree where information about prizes is revealed progressively along paths and where prize realizations are correlated via shared ancestry. It establishes that an index policy, with node-specific indices defined recursively, is optimal, and provides a constructive proof through a three-step argument that yields a discrete-choice reformulation. The author then applies this framework to a two-stage pricing game with drip pricing, deriving equilibrium prices under stage-1 and stage-2 revelation and showing that early price disclosure can lower final prices and raise consumer surplus under regulation. The findings offer a tractable, implementable approach to dynamic search problems with structured uncertainty and have practical implications for regulation and market design in contexts like monopolistic competition and e-commerce.
Abstract
I introduce and study a nested search problem modeled as a tree structure that generalizes Weitzman (1979) in two ways: (1) search progresses incrementally, reflecting real-life scenarios where agents gradually acquire information about the prizes; and (2) the realization of prizes can be correlated, capturing similarities among them. I derive the optimal policy, which takes the form of an index solution. I apply this result to study monopolistic competition in a market with two stages of product inspection. My application illustrates that regulations on drip pricing lower equilibrium price and raise consumer surplus.