When Dina Srinivasan quit her job as a digital advertising executive two years ago, she wasn’t looking to retool antitrust law for the social-media age. She just wanted to spend some time reading in coffee shops.

Then 36 years old, with a Yale law degree she had never put to use, Ms. Srinivasan spent a few months in cafes around her Connecticut home reading economic history, and mulling over her own misgivings about the evolution of the digital advertising market. One mystery nagged at her, she said: How could a company with...