i recall a few years ago, someone bought all or most of the "duty free" stores from one individual. they are just retail space rentals in the airport, like everyone else. i seem to recall being in one airport that had two competing duty frees.

from wiki:

"Duty free shopping was in its infancy when two American entrepreneurs, Charles Feeney and Robert Miller, created what is now Duty Free Shoppers (DFS) on 7 November 1960. DFS started operations in Hong Kong and spread to Europe and other places around the globe. Securing the exclusive concession for duty free sales in Hawaii in the early 1960s created a business breakthrough for DFS, and the company was positioned to focus on emerging Japanese travelers. DFS continued to innovate, expanding into off-airport duty free stores and large downtown Galleria stores and grew to become the world’s largest travel retailer. In 1996, LVMH Möet Hennessy Louis Vuitton acquired the interests of Mr. Feeney and two other shareholders and today jointly owns DFS with Mr. Miller."