[Paper Review] Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets

Haoning Xi, Didier Aussel+3 more|arXiv (Cornell University)|Jun 3, 2021

Transportation and Mobility Innovations4 citations

TL;DR

This paper proposes a single-leader multi-follower game (SLMFG) framework to regulate two-sided Mobility-as-a-Service (MaaS) markets using a name-your-own-price (NYOP) auction, where the MaaS regulator sets prices and bundles to maximize profit, while travelers and transportation service providers (TSPs) respond by optimizing participation levels. The model captures cross-group network effects and solves the resulting bilevel problems via a strong duality-based branch-and-bound algorithm, showing computational speedups of 10–100× over benchmarks.

ABSTRACT

Mobility-as-a-Service (MaaS) is an emerging business model driven by the concept of "Everything-as-a-Service" and enabled through mobile internet technologies. In the context of economic deregulation, a MaaS system consists of a typical two-sided market, where travelers and transportation service providers (TSPs) are two groups of agents interacting with each other through a MaaS platform. In this study, we propose a modeling and optimization framework for the regulation of two-sided MaaS markets. We consider a name-your-own-price (NYOP)-auction mechanism where travelers submit purchase-bids to accommodate their travel demand via MaaS platform, and TSPs submit sell-bids to supply mobility resources for the MaaS platform in exchange for payments. We cast this problem as a single-leader multi-follower game (SLMFG) where the leader is the MaaS regulator and two groups of follower problems represent the travelers and the TSPs. The MaaS regulator aims to maximize its profits by optimizing operations. In response to the MaaS regulator's decisions, travelers (resp. TSPs) adjust their participation level in the MaaS platform to minimize their travel costs (resp. maximize their profits). We analyze cross-group network effects in the MaaS market, and formulate SLMFGs without and with network effects leading to mixed-integer linear bilevel programming and mixed-integer quadratic bilevel programming problems, respectively. We propose customized branch-and-bound algorithms based on strong duality reformulations to solve these SLMFGs. Extensive numerical experiments conducted on large scale simulation instances generated from realistic mobility data highlight that the performance of the proposed algorithms is significantly superior to a benchmarking approach, and provide meaningful managerial insights for the regulation of two-sided MaaS markets in practice.

Motivation & Objective

• To address the lack of integrated, mode-agnostic pricing in MaaS systems that currently segment pricing by travel mode.
• To model the strategic interactions among MaaS regulators, travelers, and TSPs in a two-sided market under economic deregulation.
• To capture cross-group network effects—specifically supply-demand gaps—on MaaS platform performance and profitability.
• To develop an exact, scalable solution method for mixed-integer bilevel programs arising in SLMFGs with and without network effects.
• To provide managerial insights into optimal pricing and bundling strategies for MaaS regulators under heterogeneous stakeholder preferences and willingness-to-pay.

Proposed method

• Formulates the MaaS regulation problem as a single-leader multi-follower game (SLMFG), with the MaaS regulator as the leader and travelers and TSPs as two distinct follower groups.
• Employs a name-your-own-price (NYOP) auction mechanism where travelers submit purchase-bids and TSPs submit sell-bids for mobility resources.
• Models the system with and without network effects, leading to mixed-integer linear bilevel programming (MILBP) and mixed-integer quadratic bilevel programming (MIQBP) problems, respectively.
• Applies strong duality reformulation to transform the bilevel problems into single-level mathematical programs with equilibrium constraints (MPEC), enabling exact solution via branch-and-bound.
• Proposes a customized SD-based B&B algorithm that branches on binary accept/reject variables and uses three tailored branching rules for improved convergence.
• Validates the approach using large-scale simulations based on real mobility data, comparing performance against a benchmark MPEC-based B&B.

Experimental results

Research questions

• RQ1 How does the inclusion of cross-group network effects—measured as supply-demand gap—affect the profit of the MaaS regulator in a two-sided market?
• RQ2 What is the impact of bidding price range ratios (purchase and sell) on the MaaS regulator’s profit and stakeholder participation?
• RQ3 How do variations in the supply-demand gap bounds (lower and upper) influence the regulator’s profitability in the presence of network effects?
• RQ4 To what extent does the proposed SD-based B&B algorithm outperform standard MPEC-based B&B in solving large-scale SLMFGs?
• RQ5 Under what conditions do travelers’ travel costs and TSPs’ profits decrease with increasing supply-demand gap?

Key findings

• The SD-based B&B algorithm achieves computational speedups of 10 to 100 times over a benchmark MPEC-based B&B, especially for large-scale instances.
• An increase in the purchase-bidding price range ratio (b_max/b_min) increases the MaaS regulator’s profit, while an increase in the sell-bidding price range ratio (β_max/β_min) decreases it, for fixed numbers of travelers and TSPs.
• MaaS regulator profits rise with the number of travelers or TSPs when bidding price ranges are fixed, indicating scalability of the model.
• In SLMFG with network effects, profits drop significantly as the lower bound of the supply-demand gap (C̲) increases, and first slightly decrease then stabilize as the upper bound (C̄) increases.
• The presence of network effects reduces the MaaS regulator’s profit compared to the no-network-effects case, indicating a potential trade-off between market integration and profitability.
• Both travelers’ travel costs and TSPs’ profits decrease with increasing supply-demand gap, highlighting the negative impact of imbalance on stakeholder welfare.