Robustness of Online Proportional Response in Stochastic Online Fisher Markets: a Decentralized Approach
CoRR(2024)
Abstract
This study is focused on periodic Fisher markets where items with
time-dependent and stochastic values are regularly replenished and buyers aim
to maximize their utilities by spending budgets on these items. Traditional
approaches of finding a market equilibrium in the single-period Fisher market
rely on complete information about buyers' utility functions and budgets.
However, it is impractical to consistently enforce buyers to disclose this
private information in a periodic setting. We introduce a distributed auction
algorithm, online proportional response, wherein buyers update bids solely
based on the randomly fluctuating values of items in each period. The market
then allocates items based on the bids provided by the buyers. Utilizing the
known Shmyrev convex program that characterizes market equilibrium of a Fisher
market, two performance metrics are proposed: the fairness regret is the
cumulative difference in the objective value of a stochastic Shmyrev convex
program between an online algorithm and an offline optimum, and the individual
buyer's regret gauges the deviation in terms of utility for each buyer between
the online algorithm and the offline optimum. Our algorithm attains a
problem-dependent upper bound contingent on the number of items and buyers
under stationary inputs in fairness regret. Additionally, we conduct analysis
of regret under various non-stationary stochastic input models to demonstrate
the algorithm's efficiency across diverse scenarios. The online proportional
response algorithm addresses privacy concerns by allowing buyers to update bids
without revealing sensitive information and ensures decentralized
decision-making, fostering autonomy and potential improvements in buyer
satisfaction. Furthermore, our algorithm is universally applicable to many
worlds and shows the robust performance guarantees.
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