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Nash Equilibrium and Party Polarization in an Electoral Competition Model

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Abstract

We study the existence problem of Nash equilibrium as well as party polarization in an electoral competition model. In our model, political parties also value holding office (office rent) in addition to maximizing their party members’ utility. A class of models with an uncertainty about the median voter position has been increasingly important and Drouvelis, Saporiti and Vriend (2014) present an experimental study to support a model with office rent. But the inclusion of office rent renders the payoff of each party discontinuous. This makes it difficult to apply a usual fixed point argument to prove the existence of Nash equilibrium. By using a recently developed concept, C-security in McLennan, Monteiro and Tourky (2011), we provide conditions under which a pure strategy Nash equilibrium (PSE) or a mixed strategy Nash equilibrium (MSE) exists within a fairly general setting, and further the analysis by presenting conditions under which various types of policy choices, including polarization, arise in equilibrium.

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  • 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.
  • Handle: RePEc:qld:uq2004:575
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    File URL: http://www.uq.edu.au/economics/abstract/575.pdf
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    1. 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.
    2. Shino Takayama, 2007. "Office-seeking politicians, interest groups and split contributions in a campaign finance model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(4), pages 297-314.
    3. Eyster, Erik & Kittsteiner, Thomas, 2007. "Party platforms in electoral competition with heterogeneous constituencies," Theoretical Economics, Econometric Society, vol. 2(1), pages 41-70, March.
    4. Shino Takayama, 2014. "A Model of Two-stage Electoral Competition with Strategic Voters," Discussion Papers Series 525, School of Economics, University of Queensland, Australia.
    5. Alejandro Saporiti, 2008. "Existence and Uniqueness of Nash Equilibrium in Electoral Competition Games: The Hybrid Case," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(5), pages 827-857, October.
    6. Ingemar Hansson & Charles Stuart, 1984. "Voting competitions with interested politicians: Platforms do not converge to the preferences of the median voter," Public Choice, Springer, vol. 44(3), pages 431-441, January.
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    Keywords

    Noncooperative games; electoral competition; existence of equilibrium;

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