Public blockchains implement a fee mechanism to allocate scarce computational
resources across competing transactions. Most existing fee market designs
utilize a joint, fungible unit of account (e.g., gas in Ethereum) to price
otherwise non-fungible resources such as bandwidth, computation, and storage,
by hardcoding their relative prices. Fixing the relative price of each resource
in this way inhibits granular price discovery, limiting scalability and opening
up the possibility of denial-of-service attacks. As a result, many prominent
networks such as Ethereum and Solana have proposed multi-dimensional fee
markets. In this paper, we provide a principled way to design fee markets that
efficiently price multiple non-fungible resources. Starting from a loss
function specified by the network designer, we show how to compute dynamic
prices that align the network’s incentives (to minimize the loss) with those of
the users and miners (to maximize their welfare), even as demand for these
resources changes. Our pricing mechanism follows from a natural decomposition
of the network designer’s problem into two parts that are related to each other
via the resource prices. These results can be used to efficiently set fees in
order to improve network performance.

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