An aggregate NTU stability concept using one-sided money burning decentralizes stable matchings in type-based markets and extends to a random utility model with proven existence, uniqueness, and convergent algorithm.
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Matroids satisfy a generalized basis exchange where for X and Y in the symmetric difference of bases A and B there exist U and V containing them with |U|=|V| at most rank(X+Y) such that A-U+V and B+U-V are bases, plus a framework for Grassmann-Plücker extensions in characteristic-zero representable
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Aggregate Stable Matching with Money Burning
An aggregate NTU stability concept using one-sided money burning decentralizes stable matchings in type-based markets and extends to a random utility model with proven existence, uniqueness, and convergent algorithm.
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Generalizing the Multiple Exchange Property for Matroid Bases
Matroids satisfy a generalized basis exchange where for X and Y in the symmetric difference of bases A and B there exist U and V containing them with |U|=|V| at most rank(X+Y) such that A-U+V and B+U-V are bases, plus a framework for Grassmann-Plücker extensions in characteristic-zero representable