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Characterizations of Game Theoretic Solutions which Lead to Impossibility Theorems

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  • Matthew O. Jackson
  • Sanjay Srivastava

Abstract

For some game theoretic solution concepts, such as dominant strategies, Nash equilibrium, and undominated strategies, only dictatorial social choice functions are implementable on a full domain of preferences with at lest three alternatives. For other solution concepts, such as the iterative removal of weakly dominated strategies, undominated Nash equilibrium, and maximin, it is possible to implement non-dictatorial social choice functions. Which characteristics of solution concepts account for these differences? We begin by proving a new impossibility theorem. This theorem shows that conditions which are significantly weaker than strategy-proofness, assure that a social choice function is dictatorial on a full domain of preferences. This helps us to identify the essential parts of the impossibility theorems and leads to two characterization of solution concepts which lead to impossibility results. Keywords: Implementation, Social Choice.

Suggested Citation

  • Matthew O. Jackson & Sanjay Srivastava, 1992. "Characterizations of Game Theoretic Solutions which Lead to Impossibility Theorems," Discussion Papers 1004, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1004
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    1. Barbara, Salvador & Jackson, Matthew, 1988. "Maximin, leximin, and the protective criterion: Characterizations and comparisons," Journal of Economic Theory, Elsevier, vol. 46(1), pages 34-44, October.
    2. Dutta, Bhaskar & Sen, Arunava, 1991. "Implementation under strong equilibrium : A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 49-67.
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    7. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    8. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
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    Cited by:

    1. Shino Takayama & Akira Yokotani, 2017. "Social choice correspondences with infinitely many agents: serial dictatorship," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 573-598, March.
    2. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    3. Marcelo Caffera & Juan Dubra, 2005. "Getting Polluters to Tell the Truth," Microeconomics 0504008, University Library of Munich, Germany.
    4. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    5. Xiong, Siyang, 2021. "Designing referenda: An economist's pessimistic perspective," Journal of Economic Theory, Elsevier, vol. 191(C).
    6. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.
    7. Kim-Sau Chung & Jeffrey C. Ely, 2003. "Implementation with Near-Complete Information," Econometrica, Econometric Society, vol. 71(3), pages 857-871, May.
    8. Shino Takayama & Akira Yokotani, 2014. "Serial Dictatorship with Infinitely Many Agents," Discussion Papers Series 503, School of Economics, University of Queensland, Australia.
    9. 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.
    10. Hideki Mizukami & Takuma Wakayama, 2004. "Dominant Strategy Implementation in Pure Exchange Economies," Discussion Papers in Economics and Business 04-03, Osaka University, Graduate School of Economics.
    11. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    12. Takashi Kunimoto, 2006. "The Robustness Of Equilibrium Analysis: The Case Of Undominated Nash Equilibrium," Departmental Working Papers 2006-26, McGill University, Department of Economics.

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    Keywords

    implementation; social choice.;

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