# Graph-Based Equilibrium Metrics for Dynamic Supply-Demand Systems with Applications to Ride-sourcing Platforms

arXiv: https://arxiv.org/abs/2102.05805 · HTML: https://mlsanity.com/paper/2102.05805/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2021.

## Built on by (most cited first, 11 of 11)

- [Policy Evaluation for Temporal and/or Spatial Dependent Experiments](https://mlsanity.com/paper/2202.10887/) (2022)
- [Evaluating Dynamic Conditional Quantile Treatment Effects with Applications in Ridesharing](https://mlsanity.com/paper/2305.10187/) (2023)
- [Unraveling the Interplay between Carryover Effects and Reward Autocorrelations in Switchback Experiments](https://mlsanity.com/paper/2403.17285/) (2024)
- [Combining Experimental and Historical Data for Policy Evaluation](https://mlsanity.com/paper/2406.00317/) (2024)
- [Pattern Transfer Learning for Reinforcement Learning in Order Dispatching](https://mlsanity.com/paper/2105.13218/) (2021)
- [Causal Deepsets for Off-policy Evaluation under Spatial or Spatio-temporal Interferences](https://mlsanity.com/paper/2407.17910/) (2024)
- [A Two-armed Bandit Framework for A/B Testing](https://mlsanity.com/paper/2507.18118/) (2025)
- [A Unified Representation Framework for Rideshare Marketplace Equilibrium and Efficiency](https://mlsanity.com/paper/2302.14358/) (2023)
- [GeOT: A spatially explicit framework for evaluating spatio-temporal predictions](https://mlsanity.com/paper/2410.11709/) (2024)
- [Designing Time Series Experiments in A/B Testing with Transformer Reinforcement Learning](https://mlsanity.com/paper/2602.01853/) (2026)
- [Generative AI Enabled Matching for 6G Multiple Access](https://mlsanity.com/paper/2411.04137/) (2024)

## Abstract (arXiv)

How to dynamically measure the local-to-global spatio-temporal coherence between demand and supply networks is a fundamental task for ride-sourcing platforms, such as DiDi. Such coherence measurement is critically important for the quantification of the market efficiency and the comparison of different platform policies, such as dispatching. The aim of this paper is to introduce a graph-based equilibrium metric (GEM) to quantify the distance between demand and supply networks based on a weighted graph structure. We formulate GEM as the optimal objective value of an unbalanced transport problem, which can be efficiently solved by optimizing an equivalent linear programming. We examine how the GEM can help solve three operational tasks of ride-sourcing platforms. The first one is that GEM achieves up to 70.6% reduction in root-mean-square error over the second-best distance measurement for the prediction accuracy. The second one is that the use of GEM for designing order dispatching policy increases answer rate and drivers' revenue for more than 1%, representing a huge improvement in number. The third one is that GEM is to serve as an endpoint for comparing different platform policies in AB test.