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On Coalitional Stability and Single-peakedness

Author

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  • Hirofumi Yamamura

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

We study a one-dimensional voting game in which voters choose a policy from a one-dimensional policy set over which voters have single-peaked preferences. The purpose of this paper is to analyze coalitional behaviors under any given voting mechanism. We employ the notion of strong Nash equilibrium and identify a necessary and su¢ cient condition for a voting mechanism to possess a strong Nash equilibrium by using the minimax theorem. We moreover show that any strong Nash outcome, if it exists, results in an outcome recommended by a particular augmented median voter rule.

Suggested Citation

  • Hirofumi Yamamura, 2011. "On Coalitional Stability and Single-peakedness," Discussion Paper Series DP2011-21, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2011-21
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2011-21.pdf
    File Function: First version, 2011
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    Citations

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    Cited by:

    1. Louis, Philippos & Núñez, Matías & Xefteris, Dimitrios, 2023. "Trimming extreme reports in preference aggregation," Games and Economic Behavior, Elsevier, vol. 137(C), pages 116-151.
    2. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    3. Philippos Louis & Matías Núñez & Dimitrios Xefteris, 2019. "Trimming Extreme Opinions in Preference Aggregation," University of Cyprus Working Papers in Economics 12-2019, University of Cyprus Department of Economics.
    4. Hirofumi Yamamura & Ryo Kawasaki, 2013. "Generalized average rules as stable Nash mechanisms to implement generalized median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 815-832, March.
    5. Yamamura, Hirofumi, 2016. "Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 48-57.

    More about this item

    Keywords

    Single-peakedness; Augmented median voter rule; Strong Nash equilibrium; Coalition-proof Nash Equilibrium; Minimax theorem; Manipulation;
    All these keywords.

    JEL classification:

    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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