The ASA has the power to have advertisements it believes are in breach of its code of conduct withdrawn, and prevent them from appearing again. If an advertiser refuses to comply with an ASA ruling, it can impose sanctions, such as asking internet search websites to remove a marketer's paid-for search ads.
The investigation is on-going, and so the ASA declined to comment further, but one of the complainants revealed details of its response in a post on Reddit.
The investigation revolves around No Man's Sky's Steam store page, which includes assets some believe misrepresent the controversial space game.
The ASA has contacted both Hello Games and Valve and asked them to respond to a raft of questions relating to No Man's Sky advertisements.
Complaints centre around screenshots and videos that feature more advanced animal behaviour, large-scale combat and ship-flying behaviour than ended up in the launch version of the game. Complainants also say screenshots misrepresent the graphical quality of the game.
There are also complaints around the Steam store page's reference to a lack of loading screens and factions that contest territory.
While the complaints target Steam, the ASA said any ruling would apply to other advertising for No Man's Sky, such as official YouTube videos and the game's listing on the PlayStation Store.