In chapter 2, what game did Peter want to play, and what does this reveal about his character?
In Chapter 2, Peter wants to play a common game that kids play on Earth, "Buggers and Astronauts."
Peter, Ender's older brother, always chooses the role of astronaut. This means Ender has a disadvantage. In addition to Ender wearing a bugger mask that narrows his vision, Peter, who is already older, bigger, and stronger, continually taunts Ender throughout the game. As a role-play situation, Peter is acting out the attitude of humans toward buggers at that time. Everyone is taught to believe that Buggers are a sub-human species, who are dumber and weaker than humans, and also gross.
This game shows Peter's evil side. He takes everything too far. His own mallice goes beyond the game, and he picks on his younger brother from a place of raw evil inside himself. Even when Ender essentially begs for mercy, Peter won't let up. Then, at the end of it all, he laughs, and tells Ender it was just a game.
Peter demands that Ender play buggers and astronauts with him. Peter claims the role of astronaut and tells Ender to be the bugger, a member of the alien race that once attacked Earth. Ender agrees even though the bugger in this game always gets hurt.
The game Peter wants to play is buggers and astronauts. This is in Chapter 2. For chapter summaries and more go to the enotes.com study guide for 'Ender's Game'.