# Parallel Search for Information

## TL;DR

This paper analyzes the optimal stopping problem in parallel information search across multiple alternatives, providing conditions for solutions, characterizing the free boundary, and comparing parallel and sequential search strategies.

## Contribution

It establishes necessary and sufficient conditions for optimal search boundaries, characterizes their shape and asymptotic behavior, and compares parallel and sequential search strategies.

## Key findings

- Optimal search boundary is star-shaped.
- Asymptotic behavior of the value function and boundary.
- Relationship between parallel and sequential search boundaries.

## Abstract

We consider the problem of a decision-maker searching for information on multiple alternatives when information is learned on all alternatives simultaneously. The decision-maker has a running cost of searching for information, and has to decide when to stop searching for information and choose one alternative. The expected payoff of each alternative evolves as a diffusion process when information is being learned. We present necessary and sufficient conditions for the solution, establishing existence and uniqueness. We show that the optimal boundary where search is stopped (free boundary) is star-shaped, and present an asymptotic characterization of the value function and the free boundary. We show properties of how the distance between the free boundary and the diagonal varies with the number of alternatives, and how the free boundary under parallel search relates to the one under sequential search, with and without economies of scale on the search costs.