Cooperative Quests

I had an idea for a cooperative quest where players would trade quest components amongst each other, but there is a major flaw with this concept: suppose that the participants are unwilling/unable to cooperate?

Suppose, for example, that the quest is to collect playing cards, and the goal is to redeem a poker hand of five cards.  The catch is that every time that a player draws a card, they will always draw the same card.  When Gremlins draws a card, then he will always draw the Jack of Clubs.  When Moon Kitty draws a card, she will always draw the Queen of Hearts.  When Super Chicken draws a card, he will always draw a Joker.

The easiest way to complete the quest is to collect five cards of the same value, and then cash them in for five-of-a-kind.  Suppose that the quest reward payoff for five-of-a-kind was the experience equivalent to a dispatch, but something like a full house or a flush was worth the experience equivalent to a kill?  Suppose that a straight flush was worth the experience equivalent of a vanquish?

The structure of the quest is one that encourages trading cards with the community, and the reward for the quest increases by having a variety of cards.  Would you want to trade cards with others players to maximize the quest reward payoff?  What happens if a quest participant refuses to trade?

While this is a rather broad (and exaggeratedly extreme) example of the quest, it has me thinking: even though there are greater benefits to cooperation, I should never assume that everyone is willing to cooperate within a cooperative quest.