Are there repeatable or random quests?
Many RPGs, especially open-world ones, tend to have repeatable quests and/or random quests, to keep the player from running out of things to do in the game, like Skyrim or Fallout.
Does FFXV have these kinds of quests? If so, is there a list of them?
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There are no “random” quests and the only repeatable quests are the hunts, if you count those as quests.
The rescue quests, where you find people in the wilderness and give them an item or the broken down car quests arent really random. They unlock at specific chapters and points in the story. There is no indication where they are and you have to “stumble” into them, but they are always there after you reach their unlock point. They unlock in stages, so you may go past an area several times and they wont be there, then after you reach a certain point in the story, the quest will suddenly be there. This isnt random, but locked content. Many of the sidequests actually work this way, you can just see those on the map, where these two types of quests you do not.
Hunts are the only thing that is really repeatable. They arent exactly “quests” imo, as they dont count towards the sidequest trophy count. As Kerwan mentions in their comment, you get reduced rewards for every repeated hunt after the first, but you can do them as many times as you like.