Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements

TL;DR

This paper investigates online Fisher markets with sequentially arriving users, analyzing static pricing limitations and proposing adaptive algorithms that improve resource allocation efficiency using distribution knowledge or observed consumption feedback.

Contribution

It introduces the first analysis of static pricing limitations in online Fisher markets and develops adaptive pricing algorithms with enhanced performance guarantees based on distribution knowledge or observed data.

Findings

Static pricing algorithms have significant regret and capacity violation limitations.

Adaptive algorithms with distribution knowledge outperform static pricing in simulations.

Revealed preference-based adaptive algorithms show improved resource allocation in practice.

Abstract

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.