Online Resource Sharing: Better Robust Guarantees via Randomized Strategies

TL;DR

This paper introduces a randomized bidding strategy in online resource sharing that improves the robustness guarantee from 50% to approximately 59%, nearly reaching the theoretical limit, and demonstrates its near-optimality.

Contribution

It presents the first significant improvement in robust guarantees for online resource sharing using randomized strategies in repeated first-price auctions.

Findings

Achieves a 0.59-approximate guarantee of ideal utility for agents.

Shows static bidding policies cannot exceed 0.6-approximate guarantee.

Almost closes the gap to the known 0.63 hardness bound.

Abstract

We study the problem of fair online resource allocation via non-monetary mechanisms, where multiple agents repeatedly share a resource without monetary transfers. Previous work has shown that every agent can guarantee $1/2$ of their ideal utility (the highest achievable utility given their fair share of resources) robustly, i.e., under arbitrary behavior by the other agents. While this $1/2$-robustness guarantee has now been established under very different mechanisms, including pseudo-markets and dynamic max-min allocation, improving on it has appeared difficult. In this work, we obtain the first significant improvement on the robustness of online resource sharing. In more detail, we consider the widely-studied repeated first-price auction with artificial currencies. Our main contribution is to show that a simple randomized bidding strategy can guarantee each agent a $2 - \sqrt 2 \approx 0.59$ fraction of her ideal utility, irrespective of others' bids. Specifically, our strategy requires each agent with fair share $\alpha$ to use a uniformly distributed bid whenever her value is in the top $\alpha$-quantile of her value distribution. Our work almost closes the gap to the known $1 - 1/e \approx 0.63$ hardness for robust resource sharing; we also show that any static (i.e., budget independent) bidding policy cannot guarantee more than a $0.6$-fraction of the ideal utility, showing our technique is almost tight.