This is a cross post from my blog here here.
The Prisoner's Dilemma is pretty famous so I'm sure a lot of you already know what it is, but I'm going to go over it real quick anyways. There are two criminals and they have been arrested for a crime. the police want to charge them with two crimes but only have enough evidence for 1, so the police offer each prisoner a deal if they confess but if both confess then it ends up on the whole worse for both. This is what the incentives look like were the numbers are time they have to serve in prison:
Don't Confess Confess
Don't Confess (1,1) (3,0)
Confess (0,3) (2,2)
The best solution for each is that they confess and the other doesn't because if that happens then they don't serve any time, the best solution for both is that neither confess because then only 2 years total are served, but even though it results in the most time served overall and is an objectively worse outcome for both of them, both confessing is the Nash Equilibrium. They will do so because regardless of if the other prisoner does the outcomes for confess are better as they are either (1,3) compared to either (0,2). So that is the prisoner's dilemma, cooperation brings about the best outcome and yet the prisoners are incentivized to not do so. So how does this relate to loot?
In loot based games the best loot tends to come from the biggest enemies, if you team up you can fight bigger enemies but if you team up how do you split the loot? The best way to do it is that each member of the team only takes the items they can use, since different party members are going to want different kinds of loot you should be able to split it based on what each person needs, simple right? The problem is, the best solution for each person is to just take everything they can can, or at least try too.
Everyone in the party is incentivized to go after every item that drops with the mind set of 'I don't need this item but I can sell it or even trade it to someone in the party that does need it for something I do need that they scooped up'. This problem becomes even more pronounced when the other people you are playing with are people you don't know and are anonymous because then there isn't really even social pressure to cooperate. If you are playing with the same people over a period of days or weeks then you will want them to be able to pull their weight which means giving them the loot they need, but if you only need them for 30 minutes who cares if they get what they need you will never see them again.
If the goal is to get players to co-operate pitting them against each other only breeds resentment. So WoW and other MMOs instituted loot management systems. In WoW if the item is one that is theoretically best for your class (leather for rogue, plate for warrior) then you can do a special roll that only everyone who can wear the item can do and it is decided only amongst those that can wear the item who gets it. Torchlight 2 does a system where each person gets their own loot and you can't pick up other people's loot.
Not understanding what you are incentivising your players to do is a quick path to creating a toxic/negative community. There are certainly times when you want to create competition in your co-operative players and I think Zombies Ate My Neighbors is a great example of this. It is in your best interest to keep the other player alive in this game but each player has a different score based on the people they have saved, so while you wan to keep the other player alive you want to be the one saving all the people. It mostly avoids the dilemma by making the competitive aspect minor (if you still care about points after a couple levels then you are either a fool or unbelievably good at the game) and because it was a SNES game the social pressure to co-operate is there because the other player is right there.