Imagine a small group of goblins moving on the same initiative that are hit by hypnotic pattern.
When one goblin that was not affected uses its action (or an attack) to wake its ally that failed the save, can that awoken ally in turn wake another affected ally, effectively ending the spell with a chain of actions in a single turn?
Or, instead, is only one goblin able to be woken up that turn, with the waking goblin having no action to use on the next sleeping ally?
The DM decides what order creatures act when the operate on the same initiative. Therefore, the DM could rule that an awaken creature still has it's turn, and can still wake up the next one (spending 1/2 their movement to stand up, and an action to wake them up).
So: Yes, provided all creatures are all within 1/2 their movement of each other, the DM could decide (as the question suggests) that the group could end the spell on each other if even one character isn't affected.
However, if you are a DM, consider what this looks like to your players if you do this. Your player just spent a resource and their action trying to take opponents out of the fight. You then made a ruling that reduced the effect of that resource to only lasting a single turn. If I was a player and a DM did this, it would make me feel like I was really fighting the DM, rather than the goblins that the DM has put in our way. This is already a problem at a multiplicity of tables, and does not need to be exacerbated.
As a DM, if I were presented with this situation, I would say that each creature wakes up with their action already spent. They could still stand up and move 1/2 of their movement, but they could not awake another creature. This, I believe, is a more balanced approach. It allows the effect of the spell to be more powerful, but does not trivialize the encounter.
However, I suggest that you run your NPCs with no more than 2-3 creatures per initiative order, and at least 2 initiatives for each creature type. This reduces some of the swingyness of combat. You will less often have situations where all members of one side go first, and the other side is killed before they get to act.
Creatures acting on the same initiative just means that the creatures all act one after the other. Otherwise, there is no difference in the turns and what they can do with them compared with any other creatures. That means each goblin gets an action and movement. If they are able to act, they can use that action to shake another creature awake if they wish.
The DM will have to decide the order in which the creatures get to act (because they are a tied group of identical creatures that all act at the same time), but if the unaffected one end up going first he can indeed start a chain that wakes them all up.
However, do note that this implies that they are all grouped very tightly together with no enemies interfering with their movement or actions (opportunity attacks and readied actions come to mind). Additionally, they are all sacrificing their actions for the round, thus giving the PCs a big boost in action economy for the round.
This falls into one of the many gray areas of D&D rules, and it really depends upon whether you want to proceed with RAI (Rules As Intended) or RAW (Rules As Written)
RAI: I think the situation would warrant that you break down the initiative of each goblin. So at that point, I would assume that the one goblin who is awake continues to work off the pre-existing initiative. The remainder, who are asleep, should be assigned individual initiatives. While it is annoying to have all those initiatives, it is imperative for fairness in this combat. The issue you run into is exactly what you said - the players' sleep spell is hardly a hiccup for the goblins if you are able to determine their turn orders on the fly. It is my understanding that grouping like monsters to a single initiative is intended to simplify turn orders, not to have direct consequences upon various spells and features.
RAW: I don't have my books on me at the moment, but from the SRD that I found:
If a tie occurs, the GM decides the order among tied GM-controlled creatures, and the players decide the order among their tied characters. The GM can decide the order if the tie is between a monster and a player character. Optionally, the GM can have the tied characters and monsters each roll a d20 to determine the order, highest roll going first.
For RAW, you have the choice of either deciding to order the turns so as to cascade the goblins waking each other, or rolling a d20 to rank their turns henceforth. IMO this is the fairer option as it doesn't defeat what the players are attempting to do.
The DM decides initiative order for tied creatures. So the unaffected creature could decide to go first and awaken a sleeping ally. They could then go next and awaken the next and so on.
But remember it will take movement to stand up and go to the ally, and that creature's action to awaken them.
It is also possible - with a kindly DM perhaps - that a creature may simply not notice an ally is asleep as well (or not care, depending on intelligence and nature). So may decide to just attack or do something else anyway and completely ignore his poor sleeping allies, thus breaking the chain.
