Cooperation in Small Groups -- an Optimal Transport Approach

TL;DR

This paper explores how to partition populations into small cooperative groups using an optimal transport approach, establishing existence, characterization, and computational improvements for the f-core in transferable utility settings.

Contribution

It introduces a novel formulation linking f-core concepts with transportation theory, enabling new existence and characterization results and enhancing computational methods.

Findings

Established an exact existence result for f-core partitions.

Provided a characterization of f-core for general agent classes.

Improved computational methods for finite type cases.

Abstract

If agents cooperate only within small groups of some bounded sizes, is there a way to partition the population into small groups such that no collection of agents can do better by forming a new group? This paper revisited f-core in a transferable utility setting. By providing a new formulation to the problem, we built up a link between f-core and the transportation theory. Such a link helps us to establish an exact existence result, and a characterization result of f-core for a general class of agents, as well as some improvements in computing the f-core in the finite type case.