  Fisher markets are one of the most fundamental models for resource
allocation. However, the problem of computing equilibrium prices in Fisher
markets typically relies on complete knowledge of users' budgets and utility
functions and requires transactions to happen in a static market where all
users are present simultaneously. Motivated by these practical considerations,
we study an online variant of Fisher markets, wherein users with privately
known utility and budget parameters, drawn i.i.d. from a distribution, arrive
sequentially. In this setting, we first study the limitations of static pricing
algorithms, which set uniform prices for all users, along two performance
metrics: (i) regret, i.e., the optimality gap in the objective of the
Eisenberg-Gale program between an online algorithm and an oracle with complete
information, and (ii) capacity violations, i.e., the over-consumption of goods
relative to their capacities. Given the limitations of static pricing, we
design adaptive posted-pricing algorithms, one with knowledge of the
distribution of users' budget and utility parameters and another that adjusts
prices solely based on past observations of user consumption, i.e., revealed
preference feedback, with improved performance guarantees. Finally, we present
numerical experiments to compare our revealed preference algorithm's
performance to several benchmarks.
