One expansive urban center may possess a variety of distinct train systems, ranging from local intercity routes to commuter lines to extensive regional services.
When constructing a network of train tracks, stations, and timetables within this framework, ought rail operators presume that each entity functions independently, solely aiming to amplify its own profits? Or should they believe that they consistently collaborate under a unified strategy, setting aside their personal interests?
In reality, neither perspective is particularly plausible.
Scholars from MIT and ETH Zurich have created an innovative planning tool that harmonizes competition and cooperation to assist operators in a complicated, multiregional framework in strategically deciding when and how they should collaborate.
Their model is distinctive as it integrates co-investment and shared profit mechanisms that determine which collective infrastructure endeavors a participant should financially support with other operators to optimize communal advantages. The tool can aid mobility stakeholders, including governments, transport authorities, and businesses, in discerning the appropriate time for collaboration, the level of investment in joint projects, the distribution of profits, and the ramifications of withdrawing from negotiations.
“It may seem illogical, but at times you may want to invest in your competitor so that eventually, this investment will benefit you. With game theory, one can formalize this notion to generate an intriguing set of challenges,” states Gioele Zardini, the Rudge and Nancy Allen Assistant Professor of Civil and Environmental Engineering at MIT, and a leading researcher in the Laboratory for Information and Decision Systems (LIDS), affiliated with the Institute for Data, Systems, and Society (IDSS), and senior author of a study on this planning model.
Quantitative analysis demonstrates that by allocating a segment of their budget toward shared infrastructure initiatives, independent operators can achieve greater revenue than if they chose to function entirely noncooperatively.
In the case of rail operators, the researchers illustrate that co-investment also serves the users by enhancing regional train services. This mutually beneficial scenario motivates a larger number of individuals to opt for train travel, increasing profits for operators and lowering vehicle emissions, affirms Mingjia He, a graduate student at ETH Zurich and lead author.
“The essential message here is that transport network design is not a zero-sum game. One operator’s advancement doesn’t necessarily imply a loss for others. By shifting the mindset from fragmented, self-centered optimization to strategic interaction, cooperation can produce greater value for all parties involved,” she explains.
Apart from transportation, this planning framework could assist companies within a competitive sector or governments of adjacent nations in testing co-investment tactics.
He and Zardini are joined in the publication by ETH Zurich researchers Andrea Censi and Emilio Frazzoli. The findings will be showcased at the 2025 American Control Conference (ACC), with the paper selected as a finalist for the Best Student Paper Award.
Integrating cooperation and competition
Constructing transportation infrastructure within a multiregional framework generally necessitates substantial investment of time and resources. Large-scale infrastructure projects significantly impact a range of regions or operators.
Each region has its distinct priorities and decision-makers, such as local transport authorities, often leading to a lack of coordination.
“If local systems are built in isolation, regional travel might become more challenging, rendering the entire system less effective. However, if self-interested stakeholders see no benefits from coordination, they are less inclined to endorse the initiative,” says He.
To ascertain the optimal blend of cooperation and competition, the researchers applied game theory to create a framework that enables operators to align their interests and enhance regional collaboration in a manner that benefits everyone.
For example, last year, the Swiss government committed to invest 50 million euros to electrify and expand a section of a regional rail network in Germany, aiming to establish a quicker rail link between three Swiss cities.
The researchers’ planning model could aid independent entities, from state governments to rail operators, in recognizing when and how to engage in such partnerships.
The first step entails simulating scenarios where operators do not collaborate. Following that, utilizing the co-investment and shared profit mechanisms, the decision-maker can investigate cooperative strategies.
To determine a just method for dividing revenues from joint initiatives, the researchers developed a profit-sharing mechanism based on a game theory principle known as the Nash bargaining solution. This approach will establish how much benefit operators would gain in various cooperative situations, factoring in the advantages they would secure without collaboration.
The advantages of co-investment
After designing the planning model, the researchers evaluated it on a simulated transport network featuring multiple competing rail operators. They examined various co-investment ratios over multiple years to pinpoint the most advantageous decisions for operators.
Ultimately, they discovered that a semicooperative strategy yields the highest returns for all stakeholders. In one instance, by co-investing 50 percent of their total budgets into mutual infrastructure ventures, all operators maximized their returns.
In another scenario, they indicated that by investing merely 3.3 percent of their total budget in the first year of a multiyear cooperative project, operators could enhance outcomes by 30 percent across three metrics: revenue, reduced costs for consumers, and lower emissions.
“This demonstrates that a modest initial investment can result in substantial long-term advantages,” states He.
When applying their framework to more realistic multiregional networks where regions varied in size, this semicooperative approach yielded even greater results.
However, their analyses suggest that returns do not increase in a straightforward manner — occasionally raising the co-investment ratio fails to enhance benefits for operators.
Success is a complex issue reliant on the extent of investment from all operators, the selected projects, the timing of investments, and how budgets are allocated over time, He elaborates.
“These strategic choices are intricate, which is why simulations and optimization are critical for identifying the best cooperation and negotiation tactics. Our framework can support operators in making more informed investment decisions and navigate the negotiation process effectively,” she adds.
The framework could also apply to various intricate network design challenges, such as those in telecommunications or energy distribution.
In the future, the researchers aim to develop a user-friendly interface that will enable stakeholders to readily explore different collaborative alternatives. They also envision addressing more complex scenarios, like the influence of policy on shared infrastructure decisions or the resilient cooperative tactics that manage risks and uncertainties.
This research received partial funding from the ETH Zurich Mobility Initiative and the ETH Zurich Foundation.