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its a central limit order book. a curve is a big pile of bids and asks at a continuous function. updating the curve per LP would require a price time priority queue for order fills.
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To begin, let's think about central MM. The MM is a service provider to the exchange. The LP token in this framework is a representation of share of service provided (work).
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Fittingly, LP token construct democratizes the level of service provided by all LPs, to their commensurate share of the pool reserves. In a LOB, MMs whose orders at top are exposed to big market move "crests", but they are credited for contributing most for making the spread.
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In LOB exchange, you need to incentivize a lineup of diverse MMs. Exchanges show love to their traders, but their best MMs are family. Arguably there is an exclusive "LP token" club for these next of kin.
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So to answer 's thought, I think we need to consider slicing another dimension(s) not just share of asset balance, for assessing the LP's contributions to the AMM when it becomes hybrid AMM/OB style. Perhaps this may look effectively like quantile/tiers of LP tokens.
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