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On the existence of Nash equilibrium in electoral competition

Author

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  • Alejandro Saporiti

    (Queen Mary, University of London)

Abstract

This paper generalizes previous existence results on unidimensional electoral competition, by extending the traditional two-party electoral game to the case where parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. Although this game has discontinuous payoffs, it satisfies payoff security and reciprocally upper semi- continuity. However, conditional payoffs might violate quasi-concavity. Hence, our first result shows that the existence of a pure-strategy Nash equilibrium can be guaranteed only if parties' interests are symmetric. Instead, we prove that the mixed extension satisfies better reply security and, therefore, that a mixed-strategy equilibrium always exists. We also characterize the set of equilibria for a tractable version of the model. This shows that the interaction between the electoral uncertainty, the aggregate level of opportunism and its distribution among parties shape the equilibrium strategies. In particular, when the opportunism is large and asymmetrically distributed, the support of each mixed-strategy equilibrium is a closed interval located on one side of the median. Further, as the uncertainty increases, the probability distributions concentrate on the extremes of the support. And the mixed-strategy equilibrium vanishes above a critical level, over which each party plays a pure strategy in its own ideological side.

Suggested Citation

  • Alejandro Saporiti, 2005. "On the existence of Nash equilibrium in electoral competition," Game Theory and Information 0504005, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0504005
    Note: Type of Document - pdf; pages: 27
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0504/0504005.pdf
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    References listed on IDEAS

    as
    1. Coughlin, Peter J, 1990. " Majority Rule and Election Models," Journal of Economic Surveys, Wiley Blackwell, vol. 4(2), pages 157-188.
    2. Enriqueta Aragonès & Thomas R. Palfrey, 2004. "Electoral Competition Between Between Two Candidates of Different Quality: The Effects of Candidate Ideology and Private Information," Working Papers 60, Barcelona Graduate School of Economics.
    3. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    4. repec:cup:apsrev:v:77:y:1983:i:01:p:142-157_24 is not listed on IDEAS
    5. Bernhardt, Dan & Duggan, John & Squintani, Francesco, 2007. "Electoral competition with privately-informed candidates," Games and Economic Behavior, Elsevier, vol. 58(1), pages 1-29, January.
    6. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    7. Richard Ball, 1999. "Discontinuity and non-existence of equilibrium in the probabilistic spatial voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 533-555.
    8. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
    9. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    10. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    11. Aragones, Enriqueta & Palfrey, Thomas R., 2002. "Mixed Equilibrium in a Downsian Model with a Favored Candidate," Journal of Economic Theory, Elsevier, vol. 103(1), pages 131-161, March.
    12. John Ferejohn, 1986. "Incumbent performance and electoral control," Public Choice, Springer, vol. 50(1), pages 5-25, January.
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    16. John E. Roemer, 1997. "Political-economic equilibrium when parties represent constituents: The unidimensional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(4), pages 479-502.
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    More about this item

    Keywords

    Electoral competition; mixed motivations; discontinuous games; Nash equilibrium.;

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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