One large metropolis might have several different train systems, from local intercity lines to commuter trains to longer regional lines.

When designing a system of train tracks, stations, and schedules in this network, should rail operators assume each entity operates independently, seeking only to maximize its own revenue? Or that they fully cooperate all the time with a joint plan, putting their own interest aside?

In the real world, neither assumption is very realistic.

Researchers from MIT and ETH Zurich have developed a new planning tool that mixes competition and cooperation to help operators in a complex, multiregional network strategically determine when and how they should work together.

Their framework is unusual because it incorporates co-investment and payoff-sharing mechanisms that identify which joint infrastructure projects a stakeholder should invest in with other operators to maximize collective benefits. The tool can help mobility stakeholders, such as governments, transport agencies, and firms, determine the right time to collaborate, how much they should invest in cooperative projects, how the profits should be distributed, and what would happen if they withdrew from the negotiations.

“It might seem counterintuitive, but sometimes you want to invest in your opponent so that, at some point, this investment will come back to you. Thanks to game theory, one can formalize this intuition to give rise to an interesting class of problems,” says Gioele Zardini, the Rudge and Nancy Allen Assistant Professor of Civil and Environmental Engineering at MIT, a principal investigator in the Laboratory for Information and Decision Systems (LIDS), an affiliate faculty with the Institute for Data, Systems, and Society (IDSS), and senior author of a paper on this planning framework.

Numerical analysis shows that, by investing a portion of their budget into