I do not really have 'games' for my kids, (ages 3 & 5) but I have a few tips that 'usually' work well :)
The most obvious: Offer a treat for when they pick up without being told. The treat can be anything, and should be varied for best results.
Examples - I do not know the ages of children you have need for, but these would work for ages 2 to about 10, perhaps.
Small treats: Candy (of course :), gum, a cookie, reading a story, pushing them on the swing, playing a card game/board game with them, letting them paint, doing a craft with them, letting them help you make a treat etc. use your imagination ;)
Larger treats: (maybe do these after they have picked up for a number of days without a fuss) Going to the park/playground, taking them to the zoo, giving them a gift, letting them do something you normally don't, letting them skip cleaning up for one time and do it yourself... etc.
Hopefully these ideas will spark your mind to a few more that will work for your situation! Have fun!