The Rado-minor conjecture for M-natural-concave valuations

Let v:2GRv:2^{\mathcal G}\to\mathbb R be a valuation. An endowment operation with respect to TGT\subseteq\mathcal G produces the valuation v(X)=v(XT)v(T)v'(X)=v(X\cup T)-v(T), and a Rado minor valuation is one obtained from a Rado valuation by such an operation. An MM^\natural-concave valuation is a valuation in the discrete-concavity class denoted by MM^\natural-concavity. Rado-minor conjecture. Every MM^\natural-concave valuation arises as a Rado minor valuation. Rado valuations are not closed under endowment, whereas the conjectured minor class is; the source states that this conjecture is still open.

Sources & referencesView supporting material

Primary source

Jugal Garg, Edin Husic and Laszlo A. Vegh, “Approximating Nash Social Welfare under Rado Valuations”, arXiv:2009.14793 (2020).

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