Trading cycles for board games

 Trading cycles, often without the use of money, crop up here and there.  Here's an instance that was recently pointed out to me on Bluesky.

https://boardgamegeek.com/wiki/page/Math_Trades

"What is a math trade?

This is a trade between a whole bunch of people at once, using an algorithm (such as used by TradeMaximizer) to decide who should send their game to whom. Because of the algorithm used, you can only get a game you prefer over what you started with. (Or at worst, you may just keep your original game; i.e. it doesn't trade.)

This kind of trade was originally called a "mathematical no-risk trade list." Today, it's simply known as a math trade.

In a math trade, any potential trades found are always going to be "1 for 1" which is one of your offering(s) that you will ship out (or deliver if it's a "no ship") to another participant in the math trade. You will receive exactly one offering (from your "want list" for your offering) from most likely yet another participant. An "offering" is a single geeklist item, but the offering/item could be a bundle of more than one thing."

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The software link goes to one that maximizes trade volume. So these aren't top trading cycles.

But here's a survey paper on those:

1.       Morrill, Thayer, and Alvin E. Roth, “Top trading cycles,” Journal of Mathematical Economics. 112, June, 2024,   https://www.sciencedirect.com/science/article/pii/S0304406824000466