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The Max-Convolution Approach to Equilibrium Models with Indivisibilities


  • Zaifu YANG
  • Ning SUN


This paper studies a competitive market model for trading indivisible commodities. Commodities can be desirable or undesirable. Agents' preferences depend on the bundle of commodities and the quantity of money they hold. We assume that agents have quasi-linear utilities in money. Using the max-convolution approach, we demonstrate that the market has a Walrasian equilibrium if and only if the potential market value function is concave with respect to the total initial endowment of commodities. We then identify sufficient conditions on each individual agent's behavior. In particular, we introduce a class of new utility functions, called the class of max-convolution concavity preservable utility functions. This class of utility functions covers both the class of functions which satisfy the gross substitutes condition of Kelso and Crawford (1982), or the single improvement condition, or the no complementarities condition of Gul and Stacchetti (1999), and the class of discrete concave functions of Murota and Shioura (1999).

Suggested Citation

  • Zaifu YANG & Ning SUN, 2004. "The Max-Convolution Approach to Equilibrium Models with Indivisibilities," Econometric Society 2004 Far Eastern Meetings 564, Econometric Society.
  • Handle: RePEc:ecm:feam04:564

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    Cited by:

    1. Somdeb Lahiri, 2005. "Consistency and the Competitive Outcome Function," Game Theory and Information 0512002, EconWPA.
    2. Somdeb Lahiri, 2006. "Existence of Equilibrium for Integer Allocation Problems," Economics Bulletin, AccessEcon, vol. 28(14), pages 1.
    3. Somdeb Lahiri, 2005. "Existence of Equilibrium in Discrete Market Games," Game Theory and Information 0512005, EconWPA.
    4. Somdeb Lahiri, 2005. "Manipulation via Endowments in a Market with Profit Maximizing Agents," Game Theory and Information 0511008, EconWPA.

    More about this item


    Indivisibility; Equilibrium; Substitutes; Concavity;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium


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