Title: 

Cooperation and the Design of Public Goods

Abstract:

Public transit systems face two, often conflicting design goals: ridership and coverage. The ridership goal involves serving as many people as possible, typically in high-density urban centers. Conversely, the coverage goal treats transit as a social service and measures its success by how good a service it provides to those who badly need it, including those in low-density suburban areas. And while the social significance of the coverage goal has only grown after decades of increasingly suburbanized poverty, a transit agency that takes this too far is likely to face fierce pressure from those who contribute to its resources (e.g., in the form of taxes and fare collection) but do not benefit from such a service plan. This tension speaks to a fundamental difficulty with designing public goods, including but not limited to transit, that take on a social service mission while trying to maintain broad popular support.

In this talk, I will approach the design of public goods from the perspective of cooperative game theory. I will introduce non-transferable utility (NTU) linear production (LP) games, which combine the essential game-theoretic elements of public goods with the modeling flexibility of linear programming. I will show that under mild and interpretable conditions, designs that maintain popular support are possible. However, this result is existential: I will show that testing whether a particular design maintains popular support is co-NP-complete. I will also demonstrate how, while one can in principle write a mixed-integer linear programming formulation for the set of popular designs, this approach is vastly impractical even for simple instances, and that natural approaches to obtain a polyhedral relaxation through cutting plane methods can be insufficient. This motivates further research on optimizing over this complicated yet well-structured set. Lastly, I will tie this theory back to transit with a data-driven implementation that illustrates the impact of maintaining popular support on the distribution of quality of service for coverage-oriented transit designs.

Bio:

Juan Carlos Martínez Mori is a Schmidt Science Fellow and a President’s Postdoctoral Fellow with the H. Milton Stewart School of Industrial and Systems Engineering at the Georgia Institute of Technology. Prior to his current appointment, he was a Postdoctoral Fellow at the Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI) as part of their thematic program on Algorithms, Fairness, and Equity. He earned his PhD in Applied Mathematics from Cornell University in 2023 and his BSc in Civil Engineering and minor in Computer Science from the University of Illinois at Urbana-Champaign in 2017.

His primary research interests span transportation, optimization, and game theory, with additional prior work in enumerative combinatorics and sports analytics.  As a frequent transit rider, he is interested in mathematics that support more accessible and convenient public transportation.