Two-stage Stochastic Matching and Pricing with Applications to Ride Hailing (2210.11648v1)

Abstract: Matching and pricing are two critical levers in two-sided marketplaces to connect demand and supply. The platform can produce more efficient matching and pricing decisions by batching the demand requests. We initiate the study of the two-stage stochastic matching problem, with or without pricing, to enable the platform to make improved decisions in a batch with an eye toward the imminent future demand requests. This problem is motivated in part by applications in online marketplaces such as ride hailing platforms. We design online competitive algorithms for vertex-weighted (or unweighted) two-stage stochastic matching for maximizing supply efficiency, and two-stage joint matching and pricing for maximizing market efficiency. In the former problem, using a randomized primal-dual algorithm applied to a family of ``balancing'' convex programs, we obtain the optimal $3/4$ competitive ratio against the optimum offline benchmark. Using a factor revealing program and connections to submodular optimization, we improve this ratio against the optimum online benchmark to $(1-1/e+1/e^2)\approx 0.767$ for the unweighted and $0.761$ for the weighted case. In the latter problem, we design optimal $1/2$-competitive joint pricing and matching algorithm by borrowing ideas from the ex-ante prophet inequality literature. We also show an improved $(1-1/e)$-competitive algorithm for the special case of demand efficiency objective using the correlation gap of submodular functions. Finally, we complement our theoretical study by using DiDi's ride-sharing dataset for Chengdu city and numerically evaluating the performance of our proposed algorithms in practical instances of this problem.

• The paper presents a two-stage stochastic matching framework that achieves competitive ratios up to 0.767 using randomized primal-dual and factor revealing techniques.
• It develops a joint matching and pricing algorithm based on the ex-ante prophet inequality, attaining a 1/2-competitive bound and improving to (1-1/e) for demand efficiency.
• Empirical validation with DiDi’s Chengdu ride-hailing data confirms the theoretical insights, demonstrating practical improvements in market efficiency and supply optimization.

The paper, "Two-stage Stochastic Matching and Pricing with Applications to Ride Hailing," explores the critical roles of matching and pricing in two-sided marketplaces, particularly online platforms like ride-hailing services. The authors address the problem of enhancing decision-making by batching demand requests to consider imminent future demands.

Key Contributions:

1. Two-stage Stochastic Matching:
   • The paper introduces the two-stage stochastic matching problem, which aims to improve supply efficiency.
   • For this problem, the authors develop online competitive algorithms for both vertex-weighted and unweighted scenarios.
   • By using a randomized primal-dual approach applied to a set of "balancing" convex programs, the algorithms achieve an optimal $3/4$ competitive ratio compared to the offline benchmark.
   • Further improvements are made against the online benchmark, where the competitive ratio is enhanced to approximately $0.767$ for the unweighted case and $0.761$ for the weighted case. This improvement leverages a factor revealing program and ties to submodular optimization.
2. Two-stage Joint Matching and Pricing:
   • This component of the paper focuses on maximizing market efficiency by integrating both matching and pricing strategies.
   • The authors design an optimal $1/2$-competitive algorithm for joint pricing and matching. The algorithm draws upon ideas from the ex-ante prophet inequality.
   • For the specific case of a demand efficiency objective, the paper presents an improved $(1-1/e)$-competitive algorithm. This result is obtained using the correlation gap related to submodular functions.

Theoretical Methodologies:

• Randomized Primal-Dual Algorithms: Utilized to achieve competitive ratios, these algorithms are robust in balancing and optimizing variable conditions within the stochastic framework.
• Factor Revealing Programs: Such programs help improve competitive ratios by revealing factors that influence the underlying submodular optimization problems.
• Prophet Inequality Framework: Leveraged to devise algorithms that match and price jointly while maintaining optimal competitive bounds.

Practical Implications:

The paper's theoretical results are complemented by empirical evaluation using real-world data from DiDi's ride-sharing platform in Chengdu, China. This evaluation serves to validate the practical performance of the proposed algorithms, ensuring they are not only theoretically sound but also effective in real-world applications.

Summary:

This research makes significant strides in the optimization of ride-hailing platforms by addressing two-stage stochastic matching and joint matching-pricing problems. The development of competitive algorithms, both in theory and practice, offers valuable insights for enhancing market efficiency and supply optimization in complex, stochastic environments. The balance between rigorous algorithmic theory and practical applicability underscores the paper's contributions to the field of online marketplaces and ride-hailing services.