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Existence and uniqueness of Nash equilibrium in electoral competition games: The hybrid case

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This paper analyzes the traditional unidimensional, two-party electoral competition game when parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. In spite of having discontinuous payoffs, this game, refer to as the hybrid election game, is shown to be payoff secure and reciprocally upper semi-continuous. Conditional payoffs, however, are not quasi-concave. Hence, the existence of a pure strategy Nash equilibrium (PSNE) is ensured only if parties have homogenous interests in power. In that case, an equilibrium not only exists, but it is also unique. Instead, if parties have heterogeneous motivations, depending upon the relationship between the electoral uncertainty, the aggregate opportunism and its distribution across parties, a psne may or may not exist. The mixed extension, however, is always better reply secure. Therefore, a mixed strategy Nash equilibrium do indeed exist. These results generalize previous existence results in unidimensional electoral competition.

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  • Alejandro Saporiti, 2007. "Existence and uniqueness of Nash equilibrium in electoral competition games: The hybrid case," Wallis Working Papers WP50, University of Rochester - Wallis Institute of Political Economy.
  • Handle: RePEc:roc:wallis:wp50
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    Cited by:

    1. Shino Takayama & Yuki Tamura, 2015. "A Nash Equilibrium in Electoral Competition Models," Discussion Papers Series 546, School of Economics, University of Queensland, Australia.
    2. Drouvelis, Michalis & Saporiti, Alejandro & Vriend, Nicolaas J., 2014. "Political motivations and electoral competition: Equilibrium analysis and experimental evidence," Games and Economic Behavior, Elsevier, vol. 83(C), pages 86-115.
    3. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2018. "Sufficient conditions for weak reciprocal upper semi-continuity in mixed extensions of games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 99-107.
    4. Alejandro Saporiti, 2010. "Power, ideology, and electoral competition," Economics Discussion Paper Series 1003, Economics, The University of Manchester.
    5. Fournier, Gaëtan & Francou, Amaury, 2023. "Location games with references," Games and Economic Behavior, Elsevier, vol. 142(C), pages 17-32.
    6. Shino Takayama & Yuki Tamura & Terence Yeo, 2019. "Primaries, Strategic Voters and Heterogenous Valences," Discussion Papers Series 605, School of Economics, University of Queensland, Australia.
    7. Alejandro Saporiti, 2014. "Power sharing and electoral equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 705-729, April.
    8. Hummel, Patrick, 2010. "Flip-flopping from primaries to general elections," Journal of Public Economics, Elsevier, vol. 94(11-12), pages 1020-1027, December.
    9. Dimitrios Xefteris & Galina Zudenkova, 2018. "Electoral competition under costly policy implementation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(4), pages 721-739, April.
    10. Aytimur, R. Emre & Suen, Richard M. H., 2024. "Information Quality, Disagreement and Political Polarisation," MPRA Paper 121112, University Library of Munich, Germany.
    11. Shino Takayama & Yuki Tamura & Terence Yeo, 2016. "Nash Equilibrium and Party Polarization in an Electoral Competition Model," Discussion Papers Series 575, School of Economics, University of Queensland, Australia.
    12. Carrasco, Diego & Takayama, Shino & Tamura, Yuki & Yeo, Terence, 2024. "Policy polarization, primaries, and strategic voters," Mathematical Social Sciences, Elsevier, vol. 127(C), pages 19-35.

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    More about this item

    Keywords

    Electoral competition; mixed motivations; discontinuous games; Nash equilibrium.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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