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In discrete matching markets, substitutes and complements can be unidirectional between two groups of workers when members of one group are more important or competent than those of the other group for firms. We show that a stable matching exists and can be found by a two-stage Deferred Acceptance mechanism when firms preferences satisfy a unidirectional substitutes and complements condition. This result applies to both firm-worker matching and controlled school choice. Under the framework of matching with continuous monetary transfers and quasi-linear utilities, we show that substitutes and complements are bidirectional for a pair of workers.
We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing gam
We obtain a formula for the Heegaard Floer homology (hat theory) of the three-manifold $Y(K_1,K_2)$ obtained by splicing the complements of the knots $K_isubset Y_i$, $i=1,2$, in terms of the knot Floer homology of $K_1$ and $K_2$. We also present a
We propose an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from an exponential decay of the evolution semigroup combined with a time integral. We present applications to L
Let $Omega$ be the complement of a connected, essential hyperplane arrangement. We prove that every dominant endomorphism of $Omega$ extends to an endomorphism of the tropical compactification $X$ of $Omega$ associated to the Bergman fan structure on
Let $Rsubseteq E$ be two Lie conformal algebras and $Q$ be a given complement of $R$ in $E$. Classifying complements problem asks for describing and classifying all complements of $R$ in $E$ up to an isomorphism. It is known that $E$ is isomorphic to