This improv game is in the following improv game categories:
Pick a group activity, like throwing a party or organizing a picnic. One player starts, saying "Let`s ..." filling in what she wants to do. Then she starts actually doing what she said she wanted to do. A second player jumps in, saying "Let`s ..." do something else, to advance the group activity. Both players say "Yes, let`s do that" and start doing whatever suggested. Third player jumps in, suggests what to do, and again all players loudly agree to do it, and actually do it. Continue till everyone has suggested something.
See also Yes Lets - or Rather Not for a more advanced version of this exercise.
If the setup is "invent an advertising campaign for an unknown/imaginary product" then this game is also know as Also known as The Ad Game..