Matching Games with Additive Externalities

TL;DR

This paper introduces a compact additive externalities model in two-sided matchings, analyzing stability and computational complexity for various matching scenarios with new algorithms and hardness results.

Contribution

It proposes a novel additive externalities model for matchings and provides algorithms and hardness results for stability analysis.

Findings

Polynomial-time algorithms for stable matchings under additive externalities.

Computational hardness results for certain matching scenarios.

Analysis of stability under neutral, optimistic, and pessimistic behaviors.

Abstract

Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents make. Such an influence is called an externality. Whereas fully expressive representations of externalities in matchings require exponential space, in this paper we propose a compact model of externalities, in which the influence of a match on each agent is computed additively. In this framework, we analyze many-to-many and one-to-one matchings under neutral, optimistic, and pessimistic behaviour, and provide both computational hardness results and polynomial-time algorithms for computing stable outcomes.