Tight Competitive and Variance Analyses of Matching Policies in Gig Platforms
Keywords: Competitive Analysis, Variance Analyses, Online Matching, Gig Platforms
Abstract: The gig economy features dynamic arriving agents and on-demand services provided. In this context, instant and irrevocable matching decisions are highly desirable due to the low patience of arriving requests. In this paper, we propose an online-matching-based model to tackle the two fundamental issues, matching and pricing, existing in a wide range of real-world gig platforms, including ride-hailing (matching riders and drivers), crowdsourcing markets (pairing workers and tasks), and online recommendations (offering items to customers). Our model assumes the arriving distributions of dynamic agents (e.g., riders, workers, and buyers) are accessible in advance, and they can change over time, which is commonly referred to as \emph{Known Adversary Distributions} (KAD).
In this paper, we initiate variance analysis for online matching algorithms under KAD. Unlike the popular competitive-ratio (CR) metric, the variance of online algorithms' performance is rarely studied due to inherent technical challenges, though it is well linked to robustness. We focus on two natural parameterized sampling policies, denoted by $\mathsf{ATT}(\gamma)$ and $\mathsf{SAMP}(\gamma)$, which appear as foundational bedrock in online algorithm design. We offer rigorous competitive ratio (CR) and variance analyses for both policies. Specifically, we show that $\mathsf{ATT}(\gamma)$ with $\gamma \in [0,1/2]$ achieves a CR of $\gamma$ and a variance of $\gamma \cdot (1-\gamma) \cdot B$ on the total number of matches with $B$ being the total matching capacity. In contrast, $\mathsf{SAMP}(\gamma)$ with $\gamma \in [0,1]$ accomplishes a CR of $\gamma (1-\gamma)$ and a variance of $\overline{\gamma} (1-\overline{\gamma})\cdot B$ with $\overline{\gamma}=\min(\gamma,1/2)$. All CR and variance analyses are tight and unconditional of any benchmark. As a byproduct, we prove that $\mathsf{ATT}(\gamma=1/2)$ achieves an optimal CR of $1/2$.
Track: Economics, Online Markets, and Human Computation
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Submission Number: 125
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