We consider the cooperative elements that arise in the design of public goods, such as transportation policies and infrastructure. These involve a variety of stakeholders: governments, businesses, advocates, and users. Their eventual deployment depends on the decision maker's ability to garner sufficient support from each of these groups; we formalize these strategic requirements from the perspective of cooperative game theory. Specifically, we introduce non-transferable utility, linear production (NTU LP) games, which combine the game-theoretic tensions inherent in public decision-making with the modeling flexibility of linear programming. We derive structural properties regarding the non-emptiness, representability and complexity of the core, a solution concept that models the viability of cooperation. In particular, we provide fairly general sufficient conditions under which the core of an NTU LP game is guaranteed to be non-empty, prove that determining membership in the core is co-NP-complete, and develop a cutting plane algorithm to optimize various social welfare objectives subject to core membership. Lastly, we apply these results in a data-driven case study on service plan optimization for the Chicago bus system. As our study illustrates, cooperation is necessary for the successful deployment of transportation service plans and similar public goods, but it may also have adverse or counterintuitive distributive implications.

Online bipartite matching (OBM) is a fundamental model underpinning many important applications, including search engine advertisement, website banner and pop-up ads, and ride hailing. We study the independent and identically distributed (i.i.d.) OBM problem, in which one side of the bipartition is fixed and known in advance, whereas nodes from the other side appear sequentially as i.i.d. realizations of an underlying distribution and must immediately be matched or discarded. We introduce dynamic relaxations of the set of achievable matching probabilities; show how they theoretically dominate lower dimensional, static relaxations from previous work; and perform a polyhedral study to theoretically examine the new relaxations’ strength. We also discuss how to derive heuristic policies from the relaxations’ dual prices in a similar fashion to dynamic resource prices used in network revenue management. We finally present a computational study to demonstrate the empirical quality of the new relaxations and policies. Summary of Contribution: Online bipartite matching (OBM) is one of the fundamental problems in the area of online decision analysis with a wide variety of applications in operations research and computer science, for example, online advertising, ride sharing, and general resource allocation. Over the last decades, both communities have been interested in the design and analysis of new approaches. Our main contribution is to provide a polyhedral study that considers the problem’s sequential nature. Specifically, we achieve this via dynamic relaxations. We also discuss how to derive heuristic policies from the relaxations’ dual prices. We support our theoretical findings with a detailed computational study.