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Core and competitive equilibria: An approach from discrete convex analysis

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  • Yokote, Koji

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.

Suggested Citation

  • Yokote, Koji, 2016. "Core and competitive equilibria: An approach from discrete convex analysis," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 1-13.
    • Handle: RePEc:eee:mateco:v:66:y:2016:i:c:p:1-13
    DOI: 10.1016/j.jmateco.2016.06.007
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    References listed on IDEAS

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    1. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    2. Satoru Fujishige & Akihisa Tamura, 2007. "A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 136-155, February.
    3. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 251-273, May.
    4. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    5. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    6. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
    7. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
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    Cited by:

    1. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    2. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.

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