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Implementation in Economies with a Continuum of Agents

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  • Andreu Mas-Colell
  • Xavier Vives

Abstract

We study a general implementation problem for exchange economies with a continuum of players and private information, and test the robustness of the results for sequences of approximating finite economies. Assuming that the designer knows the distribution of the characteristics in the economy we consider continuous and unique implementation in both its equilibrium and dominant strategies versions and obtain results for general self-selective (first- and second-best) allocations. An upper hemicontinuity property of Bayesian equilibria of approximating economies for continuous mechanisms is demonstrated. Using this, we can, for example, conclude that if a given continuous mechanism implements uniquely a Walrasian allocation in the continuum economy then all Bayesian equilibria of large approximation economies will (with probability close to one) yield an allocation which is almost ex-post Pareto optimal.

Suggested Citation

  • Andreu Mas-Colell & Xavier Vives, 1993. "Implementation in Economies with a Continuum of Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 613-629.
    • Handle: RePEc:oup:restud:v:60:y:1993:i:3:p:613-629.
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    File URL: http://hdl.handle.net/10.2307/2298127
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    Cited by:

    1. Cordoba, Jose M. & Hammond, Peter J., 1998. "Asymptotically strategy-proof Walrasian exchange," Mathematical Social Sciences, Elsevier, vol. 36(3), pages 185-212, December.
    2. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
    3. Sahm, Marco, 2006. "Essays in Public Economic Theory," Munich Dissertations in Economics 5633, University of Munich, Department of Economics.
    4. Xavier Vives, 2011. "A Large-Market Rational Expectations Equilibrium Model," CESifo Working Paper Series 3485, CESifo.
    5. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2436-2466.
    6. Hashimoto, Tadashi, 2018. "The generalized random priority mechanism with budgets," Journal of Economic Theory, Elsevier, vol. 177(C), pages 708-733.
    7. Yan, Xinghao & Zhao, Hui, 2015. "Inventory sharing and coordination among n independent retailers," European Journal of Operational Research, Elsevier, vol. 243(2), pages 576-587.
    8. Sun, Xiang & Sun, Yeneng & Wu, Lei & Yannelis, Nicholas C., 2017. "Equilibria and incentives in private information economies," Journal of Economic Theory, Elsevier, vol. 169(C), pages 474-488.
    9. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    10. Xavier Vives, 2014. "On The Possibility Of Informationally Efficient Markets," Journal of the European Economic Association, European Economic Association, vol. 12(5), pages 1200-1239, October.
    11. J. C. Parra & M. Huggett, 2005. "Quantifying the Inefficiency of the US Social Security System," Computing in Economics and Finance 2005 70, Society for Computational Economics.
    12. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
    13. Xinghao Yan & Hui Zhao, 2011. "TECHNICAL NOTE---Decentralized Inventory Sharing with Asymmetric Information," Operations Research, INFORMS, vol. 59(6), pages 1528-1538, December.
    14. Makowski, Louis & Ostroy, Joseph M., 1992. "Vickrey-Clarke-Groves mechanisms in continuum economies : Characterization and existence," Journal of Mathematical Economics, Elsevier, vol. 21(1), pages 1-35.
    15. Kovalenkov, Alexander, 2002. "Simple Strategy-Proof Approximately Walrasian Mechanisms," Journal of Economic Theory, Elsevier, vol. 103(2), pages 475-487, April.
    16. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    17. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    18. Edward J. Green & Ruilin Zhou, 2005. "Money As A Mechanism In A Bewley Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(2), pages 351-371, May.
    19. Guesnerie, R., 1995. "The genealogy of modern theoretical public economics: From first best to second best," European Economic Review, Elsevier, vol. 39(3-4), pages 353-381, April.
    20. Tsitsiklis, John N. & Xu, Yunjian, 2015. "Pricing of fluctuations in electricity markets," European Journal of Operational Research, Elsevier, vol. 246(1), pages 199-208.
    21. Jackson, Matthew O. & Manelli, Alejandro M., 1997. "Approximately Competitive Equilibria in Large Finite Economies," Journal of Economic Theory, Elsevier, vol. 77(2), pages 354-376, December.
    22. Nehring, Klaus, 1998. "Incentive-compatibility in large games," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 57-67, January.
    23. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    24. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).

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