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Source: arxiv.org ยท
Automated market makers, first popularized by Hanson's Logarithmic Market
Scoring Rule for prediction markets, have become important building blocks
(often called 'primitives') for decentralized finance. A particularly useful
primitive is the ability to measure the price of an asset, a problem often
known as the pricing oracle problem. In this paper, we focus on the analysis of
a very large class of automated market makers, called constant function market
makers, which includes popular market makers such as Uniswap and Balancer. We
give sufficient conditions such that, under fairly general assumptions, agents
who interact with these constant function market makers are incentivized to
correctly report the price of an asset. We also derive several other useful
properties including liquidity provider returns in the path independent case.

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