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Replying to and
So: 1) MMs don't usually have the strategy of "bid and offer, never cancel, always replace", that would generally not go well 2) MMs basically always update their markets when prices move on other venues. You (and the OP) are forgetting about other exchanges.
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Replying to and
When another exchange's price drops, generally MMs on the first exchange would decrease their bids. But AMMs don't, they just sit there waiting for someone to sell to them at the pre-drop-price.
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