“…Virtual bundling has observed a steady increase from 2004 (2% of promotional offers) to 2008 (18%), and it continues to increase (A3 Distrib, 2009). According to the Panorama Trade Study, the most frequent reduction schemes in 2007 were: “buy one, get one half price” (44%), “buy two, get one free” (25%), and “buy one, get one free (BOGOF)” (9%) (Parguel, de Pechpeyrou, Sabri‐Zaaraoui, & Desmet, ; Sabri‐Zaaraoui, Parguel, & de Pechpeyrou, ). The complexity of virtual bundles increased in 2009, with virtual bundles on physical bundles, virtual bundles on already priced‐off products (Labbé‐Pinlon, Lombart, & Louis, ) and more recently with virtual bundles with quantity discounts (see Appendix ).…”