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A discrete multivariate mean value theorem with applications

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Author Info
Talman, Dolf
Yang, Zaifu (Tilburg University, Center for Economic Research)

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Abstract

We establish a discrete multivariate mean value theorem for the class of positive maximum component sign preserving functions. A constructive and combinatorial proof is given based upon a simplicial algorithm and vector labeling. Moreover, we apply this theorem to a discrete nonlinear complementarity problem and an economic equilibrium problem with indivisibilities and show the existence of solution in both problems under certain mild conditions.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 106.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:2006106

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Related research
Keywords: 47H10; 54H25; 55M20; 90C33; 91B50;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computable General Equilibrium Models
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation, Yale University. [Downloadable!]
  2. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July. [Downloadable!] (restricted)
  3. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2005. "Computing Integral Solutions of Complementarity Problems," Tinbergen Institute Discussion Papers 05-006/1, Tinbergen Institute. [Downloadable!]
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  4. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, 09. [Downloadable!] (restricted)
  5. Kaneko, Mamoru & Yamamoto, Yoshitsugu, 1986. "The existence and computation of competitive equilibria in markets with an indivisible commodity," Journal of Economic Theory, Elsevier, vol. 38(1), pages 118-136, February. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Bevia, Carmen & Quinzii, Martine & Silva, Jose A., 1999. "Buying several indivisible goods," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 1-23, January. [Downloadable!] (restricted)
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  8. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September. [Downloadable!] (restricted)
  9. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2005. "Solving Discrete Zero Point Problems with Vector Labeling," Tinbergen Institute Discussion Papers 05-106/1, Tinbergen Institute. [Downloadable!]
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  10. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, vol. 103(2), pages 411-428, April. [Downloadable!] (restricted)
  11. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2004. "Solving Discrete Zero Point Problems," Tinbergen Institute Discussion Papers 04-112/1, Tinbergen Institute. [Downloadable!]
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  1. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2008. "Solving Discrete Systems of Nonlinear Equations," Discussion Paper 2008-105, Tilburg University, Center for Economic Research. [Downloadable!]
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