The "Mr. Wolf" games that are already posted in this thread appear to be very similar to the 19th century {or earlier} Southern African American children's game "Chickama Chickama Cranie Crow".*

This game is included in Thomas W. Talley's 1922 collection of "Negro Folk Rhymes". In that book, the title given for this game is "Hawk And Chickens Play":


HAWK AND CHICKENS PLAY
{Chicken's Call} "Chickamee", chickamee, cranie crow".
I went to the well to wash my toe
When I come back, my chicken wus gone.
W'at time, ole Witch?

{Hawk sponse **} "One"
{Hawk Call} "I wants a chick."
{Chicken's Sponse} "Well, you canin't git mine".
{Hawk's Call} "I shall have a chick!"
{Chicken's Sponse} You shan't have a chick

[Thomas W. Talley, "Negro Folk Rhymes, Wise & Otherwise" {Kennikat Press Edition, 1968, p. 74; originally published, The Macmillan Company, 1922}

*The spelling "Chickama Chickama Cranie Crow" is used here as that is how that beginning rhyme of this game is most often given in the sources that I've found.

** Call & Sponse means "Call" and "Response"
In this context, "call" means the first statement in the dialogue.