Story (Does not contain puzzle content)
You've collected enough suspicious information to piece together that what you've seen is only the tip of the iceberg. There's a subtle pattern underlying the penguins' activities around the research station, but you can't fully grasp it yet. You try asking the penguins again about the odd things you've noticed, but this only makes them clam up.
While wandering the research station, feeling stuck, you notice a flyer for a market fair. You're not sure why an Antarctic research station would have one, but perhaps a bit of bartering is just what you need to spark a new idea for the negotiations.
Spoiler warning: The following story content is revealed after solving this puzzle and includes the answer to the puzzle.
That's it! If we give A SIDE OF FISH to each of the four penguin leaders, perhaps that would persuade them that we want to console them, not con them. Maybe this additional negotiation tactic will shed some light on the unexplained penguin activities.