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We consider the Arrow–Debreu exchange market model under the assumption that the agents’ demands satisfy the weak gross substitutes (WGS) property. We present a simple auction algorithm that obtains an approximate market equilibrium for WGS demands assuming the availability of a price update oracle. We exhibit specific implementations of such an oracle for WGS demands with bounded price elasticities and for Gale demand systems.more » « less
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Garg, Jugal; Husić, Edin; Li, Wenzheng; Végh, László A.; Vondrák, Jan (, Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC))
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Garg, Jugal; Husić, Edin; Végh, László A. (, Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (STOC))
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Garg, Jugal; Husić, Edin; Végh, László A. (, ACM SIGecom Exchanges)The Nash social welfare problem asks for an allocation of indivisible items to agents in order to maximize the geometric mean of agents' valuations. We give an overview of the constant-factor approximation algorithm for the problem when agents have Rado valuations [Garg et al. 2021]. Rado valuations are a common generalization of the assignment (OXS) valuations and weighted matroid rank functions. Our approach also gives the first constant-factor approximation algorithm for the asymmetric Nash social welfare problem under the same valuations, provided that the maximum ratio between the weights is bounded by a constant.more » « less
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