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An even tighter bound for the Shapley–Folkman–Starr theorem

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  • Wu, Haoyu
  • Tang, Ao

Abstract

Based on a previous refined Shapley–Folkman lemma, we derive a tighter error bound for the Shapley–Folkman–Starr theorem and apply the result to the course allocation problem.

Suggested Citation

  • Wu, Haoyu & Tang, Ao, 2024. "An even tighter bound for the Shapley–Folkman–Starr theorem," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    • Handle: RePEc:eee:mateco:v:114:y:2024:i:c:s0304406824000880
    DOI: 10.1016/j.jmateco.2024.103028
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    References listed on IDEAS

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    1. Zhou, Lin, 1993. "A Simple Proof of the Shapley-Folkman Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 371-372, April.
    2. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
    3. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    4. Budish, Eric & Reny, Philip J., 2020. "An improved bound for the Shapley–Folkman theorem," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 48-52.
    5. J. P. Aubin & I. Ekeland, 1976. "Estimates of the Duality Gap in Nonconvex Optimization," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 225-245, August.
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    Keywords

    Shapley–Folkman lemma; Error-estimation;

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