Power Struggles are random events that Uruk Captains busy themselves with in order to try and increase their power. You can interrupt a Power Struggle in order to attack a Captain when it’s advantageous to you, or, later on, you can play Uruks off each other, and interfere in Power Struggles to advance a specific Uruk at the detriment of another. Power Struggles are a good source of Power.
"Uruks frequently attempt to murder each other. If the victim survives, he will increase in power."
One Uruk and his gang will be ambushed by a host of lesser Uruks (sometimes led by a rival Captain). Either kill off the attackers, or dispose of the Captain.
"Uruks hunt vicious beasts in the wilds of Mordor to prove their strength. If successful, the leader of the hunt will increase in Power."
You can either kill the Captain on the hunt to eliminate him, or the beasts being hunted to improve his Power. Either chore is usually easier than it normally would be, since the Captain and the monster being hunted draw each other’s attention. The Captain usually hunts with a retinue.
"Uruks battle to the death to demonstrate their ferocity and to eliminate rivals. Whoever flees or dies is declared the loser while the winner will increase in Power."
As the descriptive text says, two Uruk Captains will fight it out. You can watch and eliminate the winner, aid your chosen Uruk to have them gain in Power and status, or just jump in and kill them both. You can pick up the loser’s Rune and you gain power for just attending.
"To dispense justice against traitors, enemies, and rivals, Uruks eagerly volunteer as executioners. If not stopped, the executioner will increase in Power!"
A number of Uruks will be bound, and the Captain who is the object of this quest will kill them. If he kills all of them before you kill him, Brand him, or force him to flee, he’ll gain Power.
"Uruks hold Feasts to celebrate great deeds and compete to see who can hold the most grog. If left undisturbed, the leader will increase in Power!"
The sole goal for this Power Struggle is to kill the Captain holding the Feast. It also tends to set up opportunities to poison some Grog Barrels, but aside from earning the "Black Celebration" Trophy/Achievement, there’s no reason to bother.
"Powerful Uruks will intimidate and bully others into becoming their followers. If successful, the Captain will increase in Power!"
The Captain will go around and pick a fight with other Uruks. If he kills enough of them, the rest will join him. He’ll do this a few times before he’s gained enough of a following. Depending on the type and traits of the Uruk, there’s a good chance he’ll fail against stronger types. If you help one succeed by killing the marked Uruks and staying out of sight, then kill the newly recruited Uruks and the Captain, you’ll score the Trophy/Achievement "No Power in Numbers".
Trial By Ordeal
"Uruks must prove themselves in deadly public challenges. If they survive and do not flee, they will increase in Power!"
The Uruk Captain will have a Caragor set upon him. If he wins, he becomes more powerful. If not… well, he’ll probably be dead. You can help out the Captain by shooting the Caragor to death, or give the Caragor a helping hand.
Simple and straight-forward, all you have to do for Vendetta missions is kill an Uruk. Specifically, a Captain who killed somebody on your friend’s list. You’ll have to identify the target, which will appear in a certain operational area. There’s also a random bonus objective for these missions; either killing the Captain in a set time limit, killing them from stealth, etc. Completing a Vendetta also earns you the Trophy/Achievement "Repaid in Blood".