Happy family of stable marriages

TL;DR

This paper explores various models of stable marriage, including transferable and non-transferable cases, introducing approaches to analyze intermediate scenarios and proving the existence of stable solutions.

Contribution

It introduces two approaches to partial transferable stable marriages and proves the existence of stable solutions in both fully transferable and non-transferable cases.

Findings

Existence of stable marriage in fully transferable case

Existence of stable marriage in fully non-transferable case

Introduction of two approaches for intermediate cases

Abstract

Some aspects of the problem of stable marriage are discussed. There are two distinguished marriage plans: the fully transferable case, where money can be transferred between the participants, and the fully non transferable case where each participant has its own rigid preference list regarding the other gender. We continue to discuss intermediate partial transferable cases. Partial transferable plans can be approached as either special cases of cooperative games using the notion of a core, or as a generalization of the cyclical monotonicity property of the fully transferable case (fake promises). We shall introduced these two approaches, and prove the existence of stable marriage for the fully transferable and non-transferable plans.