Skills in multiplayer Stardew have two variations:
- Skills that affect selling price apply to all players, as long as the player with that skill is online.
- Skills that affect gameplay in other ways apply only to that player.
When a player places a crab pot with either the Luremaster or the Mariner skill, the effect is tied to that crab pot. That means that the abilities will remain so long as the pot remains there, even if another player collects from it.
However, if another player without the skill breaks the crab pot and replaces it, it will no longer have the effect from the skill.