Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements
This work addresses the practical challenge of resource allocation in dynamic markets for applications like online advertising or cloud computing, but it is incremental as it builds on existing Fisher market models with adaptive enhancements.
The paper tackles the problem of computing equilibrium prices in Fisher markets under an online setting where users arrive sequentially with private information, by first analyzing the limitations of static pricing algorithms in terms of regret and capacity violations, and then designing adaptive posted-pricing algorithms that improve performance, with one algorithm achieving reduced regret and capacity violations based on revealed preference feedback.
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.