Most PvP based MMO's have some sort of incentive to play competitively. In EpicDuel's case, its for daily leaders either individually or with a faction. And in recent years, there hasn't been much else of a good reason to play competitively considering 5,000 influence in wars can be earned by most in two or three days.
My suggestion is to add Daily Rewards for Daily Leaders. For example, if you become top 5 in lets say 1v1, you get a reward package in your mail that you open and it'd give you a decent weapon or rare core, or maybe even something passive such as a double exp our double credits boost for a few hours. And of course, the winner of the daily would get a Legendary Reward that would be better versions of the common daily rewards package. A limited-rare weapon or core, or double xp or credits for 24 hours after using the item.
This would give battle-hardened competitive players a chance to grasp at something more, and it will most definitely entice others to attempt to at least become top 5 everyday. Some people would solely grind daily for weapons and cores that they aren't able to purchase. And of course, the rarest or most powerful of weapons and cores would have an EXTREMELY low drop rate from the Daily Rewards packages.
On top of this, maybe something similar could be done for factions. For example, the top Juggernaut faction for the day gets double credits for 24 hours (this nor the xp would be able to be stacked if a player were to use their own Daily Reward xp or credit boost). Or maybe even a passive for all faction members that gives them +1 strength, dex, tech, and support.
We'd see more competitive players individually, and we'd see an increase in competitive factions as everyone would surely love the boosts. The rewards I've used in this example are obviously JUST examples, but how would you guys feel about the developers adding daily rewards?