Discrete Applied Mathematics - Submodularity
Presentation and structure of substitutes valuations
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
A general two-sided matching market with discrete concave utility functions
Discrete Applied Mathematics
Mathematics of Operations Research
On the communication requirements of verifying the VCG outcome
Proceedings of the 9th ACM conference on Electronic commerce
Substitute valuations: Generation and structure
Performance Evaluation
A general two-sided matching market with discrete concave utility functions
Discrete Applied Mathematics
Algorithms for Recognizing Economic Properties in Matrix Bid Combinatorial Auctions
INFORMS Journal on Computing
Optimal allocation in combinatorial auctions with quadratic utility functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
ESA'11 Proceedings of the 19th European conference on Algorithms
Substitutes and complements in network flows viewed as discrete convexity
Discrete Optimization
Dual greedy polyhedra, choice functions, and abstract convex geometries
Discrete Optimization
Stability and competitive equilibrium in matching markets with transfers
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In their 1982 article, Kelso and Crawford proposed a gross substitutes condition for the existence of core (and equilibrium) in a two-sided matching model. Since then, this condition has often been used in the literature on matching models and equilibrium models in the presence of indivisibilities. In this paper we prove that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is anM?-concave function defined on the unit-hypercube, which is a discrete concave function recently introduced by Murota and Shioura (1999).