Core and competitive equilibria: An approach from discrete convex analysis

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    Abstract

    We extend the assignment market (Shapley and Shubik, 1972; Kaneko, 1976, 1982) by utilizing discrete convex analysis. We consider the market in which buyers and sellers trade indivisible commodities for money. Each buyer demands at most one unit of commodity. Each seller produces multiple units of several types of commodities. We make the quasi-linearity assumption on the sellers, but not on the buyers. We assume that the cost function of each seller is M-convex, which is a concept in discrete convex analysis. We prove that the core and the competitive equilibria exist and coincide in our market model.

    Original languageEnglish
    Pages (from-to)1-13
    Number of pages13
    JournalJournal of Mathematical Economics
    Volume66
    DOIs
    Publication statusPublished - 2016 Oct 1

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    Keywords

    • Assignment market
    • Competitive equilibrium
    • Core
    • Discrete convex analysis
    • M-convex function

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Applied Mathematics

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