Does anybody know how to change the ouya's resolution?

I am trying to change the resolution so I can get better
performance.

When you install xposed Mod Collection you can set the resolution down to 720p.

Sadly, it doesn’t work for me. When I turn on the 720p option in the mod collection and then reboot, my resolution stays at 1080p

What are you trying to get “better performance” with? Just curious.

I know of a couple things that do this. You may have to manually adjust it each time you want the resolution dropped. It may not be able to stay through a reboot cycle. Although I’m not certain of this.