User-Friendly Game-Theoretic Modeling and Analysis of Multi-Modal Transportation Systems

TL;DR

The paper addresses regulatory design in urban, multi-modal mobility by proposing a population-game framework that captures interactions among municipalities, mobility service providers, and travelers. It formulates mode-choice as a Nash equilibrium arising from a convex optimization of total travel costs, with costs defined as $c_{ijk}^m = p_{ij}^m + w_k t_{ij}^m$ and subject to zone-based demands and provider capacities. A key contribution is a user-friendly GUI that visualizes dynamics and computes equilibria, demonstrated through a Boston/Cambridge case with sensitivity analyses on fleet, pricing, and taxation to reveal effects on mode shares, travel time, emissions, and revenues. The work delivers a data-driven, stakeholder-inclusive tool for urban mobility design and policy evaluation, with educational utility to engage students and policymakers in complex transportation decisions.

Abstract

The evolution of existing transportation systems, mainly driven by urbanization and increased availability of mobility options, such as private, profit-maximizing ride-hailing companies, calls for tools to reason about their design and regulation. To study this complex socio-technical problem, one needs to account for the strategic interactions of the stakeholders involved in the mobility ecosystem. In this paper, we present a game-theoretic framework to model multi-modal mobility systems, focusing on municipalities, service providers, and travelers. Through a user-friendly, Graphical User Interface, one can visualize system dynamics and compute equilibria for various scenarios. The framework enables stakeholders to assess the impact of local decisions (e.g., fleet size for services or taxes for private companies) on the full mobility system. Furthermore, this project aims to foster STEM interest among high school students (e.g., in the context of prior activities in Switzerland, and planned activities with the MIT museum). This initiative combines theoretical advancements, practical applications, and educational outreach to improve mobility system design.

Figures (3)

• Figure 1: a) shows the mode-share proportion of citizens leaving zones $1$ and $2$. b) After doubling the number of buses in each zone from $15$ to $30$, the proportion of citizens traveling via bus also doubles. A mode-shift from walking to bus can be observed at the second iteration. c) Line graph showing the average travel time, municipality revenue from bus and bike tax, and CO$_2$ emissions produced during each timestep. When doubling the number of buses, the average travel time decreases and CO$_2$ emissions increase. d) Line graph showing the revenue and costs incurred by the bus company. When doubling the number of buses, costs marginally increase, but revenue significantly increases.
• Figure 2: a) shows the mode-share proportion of citizens leaving zones $5$ and $6$. b) After doubling the price of , the proportion of citizens traveling via decreases to $0\%$ due to citizens choosing a cheaper mode, which is primarily bus.
• Figure 3: Overview of the . In the leftmost column is the drop down menu for city selection, the buttons to run and re-run the simulation, an interaction menu to set parameters, and a table enumerating the zones in the city. In the center column, the user is presented with graphs showing performance metrics across simulation iterations. In the rightmost column, a "System Overview" visualizing the proportion of all citizens leaving zone $i$ traveling by mode $m$. Finally, a map allows the user to locate the studied zones geographically.

Theorems & Definitions (4)

• Definition 1: Feasible configuration
• Definition 2: Nash Equilibrium
• Theorem 1: Equilibria of the game
• Remark : Convexity and Linearity