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Game Forms with Minimal Message Spaces

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  • Reichelstein, Stefan
  • Reiter, Stanley

Abstract

This paper is concerned with the amount of communication that must be provided to implement a performance standard by a mechanism whose stationary messages have the Nash property. In p articular, the authors study implementation of Walrasian allocations in exchange environments. They show that the smallest message space t hat implements Walrasian allo-cations is one of dimension, roughly, n E (. 1 1)& ./(n 1 1), where . is the number of commodities and n the number of agents. The authors exhibit an implementing mechanism whos e message space has that dimension. Copyright 1988 by The Econometric Society.

Suggested Citation

  • Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-692, May.
    • Handle: RePEc:ecm:emetrp:v:56:y:1988:i:3:p:661-92
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    Cited by:

    1. Kenneth R. Mount & Stanley Reiter, 1996. "A lower bound on computational complexity given by revelation mechanisms (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 237-266.
    2. Scott E. Page, 2008. "Uncertainty, Difficulty, and Complexity," Journal of Theoretical Politics, , vol. 20(2), pages 115-149, April.
    3. Bernarda Zamora & Pablo Amorós, 1998. "- Implementation Of Optimal Contracts Under Adverse Selection," Working Papers. Serie AD 1998-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
    5. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 173-203, December.
    6. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-980, November.
    7. Yakov Babichenko & Leonard J. Schulman, 2015. "Pareto Efficient Nash Implementation Via Approval Voting," Papers 1502.05238, arXiv.org, revised Mar 2017.
    8. L. Hurwicz & S. Reiter, 1997. "On Transversals and Systems of Distinct Representatives," Discussion Papers 1176R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Thirumulanathan, D. & Vinay, H. & Bhashyam, Srikrishna & Sundaresan, Rajesh, 2017. "Almost budget balanced mechanisms with scalar bids for allocation of a divisible good," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1196-1207.
    10. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    11. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    12. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    13. George F. N. Shoukry, 2019. "Outcome-robust mechanisms for Nash implementation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 497-526, March.
    14. Rayati, Mohammad & Teneketzis, Demosthenis, 2022. "Electricity market design and implementation in the presence of asymmetrically informed strategic producers and consumers: A surrogate optimization-based mechanism," Energy Economics, Elsevier, vol. 109(C).
    15. J. Jordan, 2009. "Communication complexity and stability of equilibria in economies and games," Review of Economic Design, Springer;Society for Economic Design, vol. 13(1), pages 115-135, April.
    16. Arya, Anil & Mittendorf, Brian, 2005. "Using disclosure to influence herd behavior and alter competition," Journal of Accounting and Economics, Elsevier, vol. 40(1-3), pages 231-246, December.
    17. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 1-14, December.
    18. Segal, Ilya, 2007. "The communication requirements of social choice rules and supporting budget sets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 341-378, September.
    19. Ilya Segal, 2004. "The Communication Requirements of of Social Choice Rules and Supporting Budget Sets," Economics Working Papers 0039, Institute for Advanced Study, School of Social Science.
    20. Ramesh Johari & John N. Tsitsiklis, 2009. "Efficiency of Scalar-Parameterized Mechanisms," Operations Research, INFORMS, vol. 57(4), pages 823-839, August.
    21. Marschak, Thomas, 2006. "Organization Structure," MPRA Paper 81518, University Library of Munich, Germany.
    22. Dilip Mookherjee, 2008. "The 2007 Nobel Memorial Prize in Mechanism Design Theory," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(2), pages 237-260, June.
    23. Mehmet Barlo & Nuh Aygün Dalkıran, 2022. "Computational implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 605-633, December.

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