
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.
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Taxonomy
TopicsGame Theory and Voting Systems · Economic theories and models · Game Theory and Applications
