Various is the correct author for any book with multiple unknown authors, and is acceptable for books with multiple known authors, especially if not all are known or the list is very long (over 50).
If an editor is known, however, Various is not necessary. List the name of the editor as the primary author (with role "editor"). Contributing authors' names follow it.
Note: WorldCat is an excellent resource for finding author information and contents of anthologies.
Enjoy all the Mother Goose nursery rhymes all in one place in this oversized treasury. The thick pages will sure to be a favorite with young readers wanting to look at the brightly colored pictures. Each rhyme has its own devoted page complete with graphics by many different illustrators. This is sure to be a night time read-aloud pick. This collection contains many of the most popular tales such as Little Bo-Peep, Old MacDonald, and Mary Had a Little Lamb, but also some obscure ones like Sleep Tight and Freddie and the Cherry Tree. The end pages are illustrated in clouds as is the front and back inside covers and coordinating jacket. I would use this book in a 2nd grade ‘now and long ago’ unit or in a 4th grade poetry lesson. Target audience: PreK-4th.