Manipulating the outcome of stable matching and roommates problems
Krist\'of B\'erczi, Gergely Cs\'aji, Tam\'as Kir\'aly

TL;DR
This paper explores methods to modify or extend preferences and instances in stable matching and roommates problems to ensure stability or desired properties, analyzing complexity and approximation limits.
Contribution
It provides new complexity results, approximation algorithms, and insights into modifying preferences and instances for stable matchings.
Findings
Removing agents from odd cycles is optimal in certain cases
Modifying preferences is hard to approximate within a factor of 2
Polynomial algorithms exist for bipartite cases with preference modifications
Abstract
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet certain requirements. In such cases, one might be interested in modifying the instance so that the existence of a stable outcome with the desired properties is ensured. We focus on three different modifications. In stable roommates problems with all capacities being one, we give a simpler proof to show that removing an agent from each odd cycle of a stable partition is optimal. We further show that the problem becomes NP-complete if the capacities are greater than one, or the deleted agents must belong to a fixed subset of vertices. Motivated by inverse optimization problems, we investigate how to modify the preferences of the agents as little as…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications
