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**Mixed equilibrium in a Downsian model with a favored candidate.**
*(English)*
Zbl 1050.91028

Two candidates simultaneously choose positions on a finite set of points in a one-dimensional policy space. A voter votes for the candidate closest to his or her ideal policy position. If there are no extraneous factors, both candidates adopt a median position and each has a \(\frac{1}{2}\) probability of winning. However, in normal elections, extraneous factors do intrude. In this paper the authors analyze the situation where one candidate enjoys an ‘image’ advantage over the other. The advantage is taken to be constant for all voters. The principal focus of the authors is the situation where the image advantage is small (less than the distance between the points in the policy-space). The authors show that under certain assumptions, the candidate with the advantage chooses a centralist policy stance, but the equilibrium strategy is mixed, while the disadvantaged candidate chooses a mixed U-shaped strategy to establish the distance from the advantaged candidate. The pure strategy result when there is no advantage is shown to be a degenerate limiting case as the advantage tends to zero.

Reviewer: Duncan J. Melville (Canton)

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\textit{E. Aragones} and \textit{T. R. Palfrey}, J. Econ. Theory 103, No. 1, 131--161 (2002; Zbl 1050.91028)

### References:

[1] | Adams, J., Policy divergence in multicandidate probabilistic spatial voting, Public Choice, 100, 103-122 (1999) |

[2] | Ansolabehere, S.; Snyder, J. M., Valence politics and equilibrium in spatial election models, Public Choice, 103, 327-336 (2000) |

[3] | Aragones, E.; Palfrey, T. R., Mixed equilibrium in a Downsian model with a favored candidate, Working Paper 502 (October 2000) |

[4] | Banks, J. S.; Kiewiet, D. R., Explaining patterns of candidate competition in congressional elections, Amer. J. Polit. Sci., 33, 997-1015 (1989) |

[5] | Berger, M. M.; Munger, M. C.; Potthoff, R. F., With uncertainty, the Downsian model predicts divergence, J. Theoret. Polit., 12, 262-268 (2000) |

[6] | Bernhardt, D.; Ingberman, D., Candidate reputations and the incumbency effect, J. Public Econ., 27, 47-67 (1985) |

[7] | Dasgupta, P.; Maskin, E., The existence of equilibrium in discontinuous economic games I: Theory, Rev. Econ. Stud., 53, 1-26 (1986) · Zbl 0578.90098 |

[8] | Downs, A., An Economic Theory of Democracy (1957), Harper and Row: Harper and Row New York |

[9] | Erikson, R.; Palfrey, T. R., Equilibrium effects in campaign spending games: Theory and data, Amer. Polit. Sci. Rev., 94, 595-610 (2000) |

[10] | GAMBIT software, http://www.hss.caltech.edu/gambit; GAMBIT software, http://www.hss.caltech.edu/gambit |

[11] | Glicksberg, I. L., A Further generalization of the kakutani fixed point theorem with application to Nash equilibrium points, Proc. Amer. Math. Soc., 38, 170-174 (1952) · Zbl 0046.12103 |

[12] | Groseclose, T., Character, charisma, and candidate locations: Downsian models when one candidate has a valence advantage, Working Paper (1999) |

[13] | Ingberman, D., Incumbent reputations and ideological campaign contributions in spatial competition, Math. Comput. Model., 16, 147-169 (1992) · Zbl 0757.90009 |

[14] | Kiewiet, D. R., Macroeconomics and Micropolitics (1983), Univ. of Chicago Press: Univ. of Chicago Press Chicago |

[15] | Kiewiet, D. R.; Zeng, L., An analysis of congressional career decisions, 1947-86, Amer. Polit. Sci. Rev., 87, 928-941 (1993) |

[16] | Londregan, J.; Romer, T., Polarization, incumbency, and the personal vote, (Barnett, W. A.; Hinich, M. J.; Schofield, N. J., Political Economy: Institutions, Competition, and Representation (1993), Cambridge Univ. Press: Cambridge Univ. Press Cambridge), 355-377 |

[17] | Popkin, S.; Gorman, J. W.; Phillips, C.; Smith, J. A., Comment: What have you done for me lately? Toward an investment theory of voting, Amer. Polit. Sci. Rev., 70, 779-805 (1976) |

[18] | Sion, M.; Wolfe, P., On a game without a value, Contributions to the Theory of Games, III, Princeton Annals of Mathematical Studies No. 39 (1957), Princeton University Press: Princeton University Press Princeton, p. 299-306 · Zbl 0078.33105 |

[19] | Stokes, D. E., Spatial Models of Party Competition, Amer. Polit. Sci. Rev., 57, 368-377 (1963) |

[20] | Wittman, D., Candidate Quality, Pressure Group Endorsements, and Uninformed Voters, Working Paper (2000) |

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