If a coin is spent twice at the same time, what happens?

This question was asked at chia_network.public on Keybase.

The nodes will prefer the one with the higher fee. If one happens after the first one goes through, it will fail due to a double spend.

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Some additional nuance. If the transaction is exactly the same, the higher fee one will win. If the transaction has slightly different coins in it, then the first one into the mempool wins.