Sun Dec 30, 2018 12:26 am
Titanfall 2 seems to fit your description. Otherwise, there really aren't games like you're asking for, with competitive multiplayer with bots available that also includes an open world singleplayer. There especially won't be much of any such games that less than 5 years old. Check at Far Cry 4 if you're up to it if you enjoyed 5.
Try Sniper Elites 2, 3, and 4. They're third person stealth sniper games that can be played more like action games. 2 isn't too open world but it's fun. 3 and 4 are much more open with some huge open maps which give you objectives and let you complete them any way you like and are a good time in singleplayer. They do have some limited cooperative multiplayer with bots, but no competitive multiplayer against bots.
I recommend you check out Dead Island and it's superior successor Dying Light if you aren't opposed to zombie games. Dying Light especially is a load of fun and can be played Cooperatively with friends or alone. Don't be put off by reviews about Dead Island being glitchy, most of the bugs got patched out after people already made their reviews, and it runs and plays well now.
Fallout 4 is singleplayer only but pretty good despite many people's dislike for it because it doesn't "feel like a fallout game". It's a good play in its own right.
Borderlands 2 might fit the bill as well. It's not really multiplayer but is cooperative (it's best with coop though so you may want to skip it if you don't have people who will play it with you).
Grand Theft Auto 5 singleplayer is pretty good as well, but again, no multiplayer with bots.
Deus Ex: Human Revolution is older but a good singleplayer though it's more linear. Deus Ex: Mankind Divided is a little more open world but with linear segments. Though again neither of those two are multiplayer.