Paper plates, especially the less expensive kind, are not very strong. Because of this, they may bend, fold, or just plain collapse at the worst of times, making you spill your food on the table, ground, or even worse, on somebody. If you want to avoid these types of accidents, you could use paper plate holders. This are plastic discs that go under the paper plate, and serve as a sort of base, helping your plate stay flat.
Here’s an example, but I wish it was available in a different color:
Plastic Paper Plate Holder pictured: Classic Red 10-3/8″ Plastic Paper Plate Holders, Set of 4 by Greenbrier International Inc
Pictured above: 1- Mr. Bar-B-Q, Inc. 40181X Paper Plate Holders, Pack of 4 2- Reusable Plastic Paper Plate Holders Set Of 4 Blue Shade May Vary by Greenbrier International 3- Plastic Paper Plate Holders, Set of 4(blue) by Cooking Concepts 4-Paper Plate Holders, 4 Packs, Great Outdoors (2, Red/Blue) 5- Barbecue, Party, Picnic; Sturdy Reusable Paper Plate Holders & Heavy Duty Flatware by Living Solutions