That might be related to time discounting rates. For example, if the paperclipper has a low discounting rate (a paperclip today has the same utility as two paperclips in 100 years), and the power-hungry AI has a high discounting rate (a 25% chance of ultimate power today has the same utility as a 50% chance tomorrow), then I guess the paperclipper will tend to win. But for that contest to happen, the two AIs would need to arise almost simultaneously. If one of the AIs has a head start, it will try to takeoff quickly and stop other AIs from arising.
That might be related to time discounting rates. For example, if the paperclipper has a low discounting rate (a paperclip today has the same utility as two paperclips in 100 years), and the power-hungry AI has a high discounting rate (a 25% chance of ultimate power today has the same utility as a 50% chance tomorrow), then I guess the paperclipper will tend to win. But for that contest to happen, the two AIs would need to arise almost simultaneously. If one of the AIs has a head start, it will try to takeoff quickly and stop other AIs from arising.