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Existence of Equilibrium for Integer Allocation Problems

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  • Somdeb Lahiri

    (CAFS IFMR)

Abstract

In this paper we show that if all agents are equipped with well-behaved discrete concave production functions, then a feasible price allocation pair is a market equilibrium if and only if it solves a linear programming problem. Using this result we are able to obtain a necessary and sufficient condition for existence that requires an equilibrium price vector to satisfy finitely many inequalities. A necessary and sufficient condition for the existence of market equilibrium when the maximum value function is Weakly Monotonic at the initial endowment that follows from our results is that the maximum value function is partially concave at the initial endowment. We also provide a discussion of the results and an alternative solution concept. The alternative solution concept is however, informationally and computationally inefficient.

Suggested Citation

  • Somdeb Lahiri, 2006. "Existence of Equilibrium for Integer Allocation Problems," Computing in Economics and Finance 2006 8, Society for Computational Economics.
    • Handle: RePEc:sce:scecfa:8
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    References listed on IDEAS

    as
    1. Zaifu YANG & Ning SUN, 2004. "The Max-Convolution Approach to Equilibrium Models with Indivisibilities," Econometric Society 2004 Far Eastern Meetings 564, Econometric Society.
    2. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    4. Peter R. Wurman & Michael P. Wellman, 1999. "Equilibrium Prices in Bundle Auctions," Working Papers 99-09-064, Santa Fe Institute.
    5. Somdeb Lahiri, 2005. "Manipulation via Endowments in a Market with Profit Maximizing Agents," Game Theory and Information 0511008, University Library of Munich, Germany.
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    More about this item

    Keywords

    existence; market equilibrium; discrete concave; linear programming;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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