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- W4287702986 abstract "The set of stable matchings induces a distributive lattice. The supremum of the stable matching lattice is the boy-optimal (girl-pessimal) stable matching and the infimum is the girl-optimal (boy-pessimal) stable matching. The classical boy-proposal deferred-acceptance algorithm returns the supremum of the lattice, that is, the boy-optimal stable matching. In this paper, we study the smallest group of girls, called the {em minimum winning coalition of girls}, that can act strategically, but independently, to force the boy-proposal deferred-acceptance algorithm to output the girl-optimal stable matching. We characterize the minimum winning coalition in terms of stable matching rotations and show that its cardinality can take on any value between $0$ and $leftlfloor frac{n}{2}rightrfloor$, for instances with $n$ boys and $n$ girls. Our main result is that, for the random matching model, the expected cardinality of the minimum winning coalition is $(frac{1}{2}+o(1))log{n}$. This resolves a conjecture of Kupfer cite{Kup18}." @default.
- W4287702986 created "2022-07-26" @default.
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- W4287702986 date "2020-07-30" @default.
- W4287702986 modified "2023-10-16" @default.
- W4287702986 title "Descending the Stable Matching Lattice: How many Strategic Agents are required to turn Pessimality to Optimality?" @default.
- W4287702986 doi "https://doi.org/10.48550/arxiv.2007.15748" @default.
- W4287702986 hasPublicationYear "2020" @default.
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