Cooperation and the Design of Public Goods

TL;DR

This paper models cooperation in public goods design using non-transferable utility linear production games, analyzing core properties, computational complexity, and applying the framework to transportation policy optimization.

Contribution

It introduces NTU LP games to formalize strategic cooperation in public goods, providing structural insights, complexity results, and a practical case study.

Findings

Core non-emptiness conditions identified

Core membership decision is co-NP-complete

Algorithm developed for social welfare optimization

Abstract

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.