What new game do Jem, Scout, and Dill come up with in To Kill a Mockingbird?

Jem, Scout and Dill play a new game where they act out Boo Radley’s life story.

Jem, Scout and Dill like to playact.  They take stories from movies or books and act them out in the yard.  Dill is so fascinated with the story of the neighborhood bogeyman Boo Radley that they decide to use his life as inspiration for their plays.  Their story is “woven from bits and scraps of gossip and neighborhood legend.”  Scout plays Mrs. Radley, Dill plays Mr. Radley, and Jem hams it up as a crazy young Boo.

As the summer progressed, so did our game. We polished and perfected it, added dialogue and plot until we had manufactured a small play upon which we rang changes every day. (Ch. 4)

Atticus does not approve of the game.  He tells the children to leave the Radleys alone.  Scout is sure that Boo can see them and is at first afraid to take part in the game.   Atticus just feels that the Radleys have been victimized enough.  He does not want his children acting out town gossip for all to see.

Atticus’s arrival was the second reason I wanted to quit the game. The first reason happened the day I rolled into the Radley front yard. Through all the headshaking, quelling of nausea and Jem-yelling, I had heard another sound, so low I could not have heard it from the sidewalk. Someone inside the house was laughing. (Ch. 4)

Clearly, Boo Radley is entertained by the game.  He probably thinks it is funny that someone is taking an interest in him.  He leads a lonely life as a recluse, and he enjoys watching the children.  He comes to be protective of them, carefully leaving the safety of his house to hide presents for them, looking out for them, and finally saving their lives when Bob Ewell attacks them.