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Unfortunately I think it’s only wolves

There is no feature for auctioning food, however, you could auction said food in a forum auction.

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You could have a bulk auction on food in the forums. In which, bidders would be bidding for, say, 10 rabbits in a bundle. After the winning bid amount is sent to you, you would use the 'Gift Food to Another Pack' function to send them food - however, this is not reasonable for bulk buying, + is time-consuming.

While possible, the neat answer to the question is, no, there is not a way to auction food as an official feature.

Hm, it's weird though, that might violate our 'don't offer what you don't have' rule, because x amount of feedings get stolen every night. But because it's a game mechanic I guess it would be ok.

This.

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Exactly my point in the smaller bundles - to auction the materials they need to be just as secure as a 'regular' item/object/etc. that can be secured, like a wolf.

I've auctioned food bundles off with absolutely no problem! You just NEED to make sure you have all food available when the auction ends. What I did was make sure I had a ton of extra of that food type.

Example: auctioning off a bundle of elk (5 in a bundle). I would have at least 15 elk to account for any stolen. I would also be actively exploring to make sure I keep that number up