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

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Abstract

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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    1. repec:cup:apsrev:v:87:y:1993:i:02:p:382-392_10 is not listed on IDEAS
    2. repec:cup:apsrev:v:77:y:1983:i:01:p:142-157_24 is not listed on IDEAS
    3. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 573-585, June.
    4. Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477.
    5. Hinich, Melvin J., 1977. "Equilibrium in spatial voting: The median voter result is an artifact," Journal of Economic Theory, Elsevier, vol. 16(2), pages 208-219, December.
    6. 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.
    7. 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.
    8. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    9. 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.
    10. John Ferejohn, 1986. "Incumbent performance and electoral control," Public Choice, Springer, vol. 50(1), pages 5-25, January.
    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. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    13. 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.
    14. Duggan, John & Fey, Mark, 2005. "Electoral competition with policy-motivated candidates," Games and Economic Behavior, Elsevier, vol. 51(2), pages 490-522, May.
    15. 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.
    16. 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.
    17. Jean-FranÚois Laslier, 2000. "Interpretation of electoral mixed strategies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 283-292.
    18. Ignacio Ortuño Orti´n, 2002. "Ideological versus Downsian political competition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 551-567.
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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. Alejandro Saporiti, 2010. "Power, ideology, and electoral competition," The School of Economics Discussion Paper Series 1003, Economics, The University of Manchester.
    4. 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.
    5. Hummel, Patrick, 2010. "Flip-flopping from primaries to general elections," Journal of Public Economics, Elsevier, vol. 94(11-12), pages 1020-1027, December.
    6. repec:spr:sochwe:v:50:y:2018:i:4:d:10.1007_s00355-017-1103-3 is not listed on IDEAS
    7. 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.

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    Keywords

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

    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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