Give some incentive for players to create partys.
In my opinion there should be some incentive to create a party and not just so u can do co-op play.
For that i would have 2 suggestions.
1. First suggestion would be to adjust the rate of crown drops a bit when u go in with a bigger party (the increase in crown drops should be roughly about 35-45 Percent per player in the party in my opinion so that solo runners still get alot more crowns out of one depth but teamplayers should have enough crown drops to keep going too in lower lvls).
2. Second suggestion would be to lower energy costs of elevators for partys with more ppl. Example 2 ppls =8 energy, 3 ppls=6 energy, 4 ppls=4 energy.
I would say that just using one of those suggestions would greatly increase the willingness of ppl to create partys in lower depth too.
If you die alone, you have to pay to revive.
If you die with friends, they can pick you up!
That's enough for most people.
The motivation to play with a party is simply fun, and makes certain tasks easier.
And as Paska and Magnus stated, reviving players for free.
And it's highly recommended to have a party in Tier 3.
In a typical MMO, do you fight the newest superboss solo? No, you fight it with a party.
Currently I like the system. You don't lose heat when you're with a party. However, I rarely join pugs anymore. I need to have the ability to kick whoever I want because enemies health multiplies by every person present. So if I'm in a party of 4 and I'm doing all the work than I'm doing 4 times the work and it's time to start kicking people. If I had to change anything I would make it so enemies gained a little less hp per person on a floor. That hp bonus makes killing a healer an absolute pain.
Another advantage to playing in a party is that only the hp of the monsters is increased, not the actual amount of monsters. So instead of 1v10 it's 4v10.

Censor has a good point. A pick-up group and a party of friends are quite different animals.
As someone who had only joined recently, I found myself suffering through the early symptoms of not having a consistent friend list; I won't bother listing all of them but I'm sure some of you can remember an encounter with the occasional lag-monster, a bare-minimum dead-corpse-freeloader or, my favorite, the creature from the 30sec-afk lagoon. Seriously, I think that guy was playing the game while texting and racing a motorcycle on a sinuous cliff-side road.
For casual players, the sense of being able to progress despite a completely erratic and inconsistent play-schedule is incredibly important and basically what attracted me to this mmo (which gets so many things right!) but there are few things more frustrating than seeing what little spare time I fought with my life for being wasted on unproductive runs due to the random liabilities of a random party. As such, I ended up soloing my way pretty much exclusively until the wipe became imminent and everyone felt like experimenting with their energy.
Now don't get me wrong, the majority of the people I met were competent, helpful and friendly, and I understand that the spontaneous, random and dynamic co-op experience is the point of this game being multiplayer but the problem is that it's only one single player in the group that can ruin everyone's day. Perhaps, what the devs could implement here is to give every party member (as opposed to just the group leader) the ability to leave the group without being kicked to haven and wasting the energy it took to reach that position without making it to your goal. This way, people would feel much safer rolling the dice into a random group without having to marry it and it also encourages all members to pull their own weights since the party leader can't take everyone else's energy investment hostage.
I strongly agree with the OP. Right now there is not enough incentive to form parties, especially if farming for specific loot or recipes. Let's compare 2 players running in a party vs splitting up and running in two separate instances.
Current advantages of solo play:
- Monsters die more easily (less hp per).
- More loot gained (monster drops and powerups aren't split).
- More recipes discovered (2x more crossroads visited per run).
Current advantages of group play:
- Better odds, fewer monsters focusing on any one player.
- The potential for free revives
So, if you're doing farming runs it actually makes sense to split up even if you have a friend to play with. You'll generate the same number of coins and the same heat per run but you'll get twice the drops and discover twice the recipes. Simply put, this stinks. Party play is effectively discouraged unless you're doing content that's dangerous for your gear.
I strongly believe that mobs should drop more crowns and loot per player added to the party to counteract this.

Party play also gets 4x minerals, and can bring in a greater variety of gear.
Why does party play need to be encouraged more than it is now? What's wrong with playing solo and chatting in Haven in between runs?

I have to agree with your points tbh....
Only reason I ever solo T3 - If I know I want to waste 80ce, and not finish the whole run....if its a run with an arena towards the end I usually wont finish since the cost of revives wont make up for my gains.
Only Reason to solo T2 - Its a bit faster, but honestly its pretty boring.
My View, (Coming from someone who does solo a bit)
1. It gets BORING
2. Even if you have the Ce its not worth it since you dont make half the cash back.
3. It is not faster.....I solo'd and usually if I dont solo I end up going faster with 1 or 2 more partners. If you solo alone you mainly dont want to die so you do a lot of vial throwing, shooting, and bombing and less sword action.
Playing solo is a much different experience than playing in a party. You have to be much more canny, as there's no one to cover your back if something goes wrong, like a stronger healer showing up or you get ambushed. If you get into gate construction, the amount of minerals gathered while playing solo is pitiful compared to group yields.
Currently my main motivation for needing a party is if I want to go into the deeper parts of Tier 2, and even moreso for Tier 3, because even though loot is split up, you can get rarer loot, which is absolutely essential for crafting the higher level armors. In comparison, the loss of crowns isn't as much of a detriment since the cost of crafting versus outright buying gets insane towards 3-star and above items.
So I think that's reason enough for wanting to join a party.
I think a good approach towards building a reliable friends list is to join parties and see whose playstyles are compatible with yours.

I'm not going to lie, I would love to see this game become more of a co-operative experience.
There's a lot of potential for those kinds of puzzles and it's just a realm left unexplored.
It's something I would personally like to see.
Some notes about party play:
-Reviving someone with your health gives you 30% of their current heat.
-Crowns/heat aren't split, although they're shared - So pretty much, no matter how many players you have in the party, you'll get the same amount of crowns and heat yourself.
-Monsters gain more health and damage. (mostly health)
-Hearts drop more often.
-Materials drop more often.
Honestly, with all those reasons, I find it more fun, challenging (sometimes easier), with teamplay. Of course, as long as you don't get terrible members that die every two seconds. Even with the health/damage increase, it's not that big of a problem - Me and Magnus still managed to easily duo Vanaduke, even on a four player party, for example. (yep, the others were dead and doing nothing! :< )
@Shoebox - George (The dev that works on level design... Is that his name?) has actually commented that he was working on teamwork levels and the such one time.
After Tier 1, and really even in Tier 1, but more noticeable by Tier 2 and beyond is the fact that going through the floors with a team is much more beneficial. You die less, if you do die, you can be revived for free (no Energy used). I think there is really incentive enough to play the harder parts of this game with groups, friends, guild members etc...
Secondly why would we discourage 1 player play, shouldn't players be free to play this game how they want? Whether it be alone or in a group of 2 - 4?