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.

You should access OUYA through ADB.

1:
adb shell

2:
$ su

3:
mount -o rw,remount -t ext4 /dev/block/platform/sdhci-tegra.3/by-name/APP

4:
vi /system/build.prop

5:
Use the arrows key to navigate and before the last block of the file, press i to change to input mode and include this line:

persist.tegra.hdmi.resolution=720p

6:
:wg to save the changes.

7:
exit
exit

8:
adb reboot

Does this work to persist the change? Have you tested it?