Abstract
Two incumbent parties choose their platforms in a unidimensional policy space while facing a credible threat of an entry by the third party. Relative electoral support is the predominant objective of each party, and the third party enters only if it can displace one of the incumbents by receiving at least the second highest support. We prove the existence and uniqueness of an equilibrium for a wide class of distributions of voters’ ideal points, including, in particular, log-concave distribution functions. Moreover, in an equilibrium the incumbents prevent the entry and achieve the “balance of power” by choosing distinct positions in the policy space and equally splitting the electorate.
We would like to thank Michel Le Breton and Jean-François Mertens for their useful comments. A part of the paper was written when the first author was visiting CORE, the hospitality of which is greatly appreciated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alvarez, R.M., Nagler, J.: A new approach for modeling strategic voting in multiparty elections. Br. J. Pol. Sci. 30, 57–75 (2000)
Bergstrom, T., Bagnoli, M.: Log-concave probability and its applications. Econ. Theory 26, 445–469 (2005)
Cohen, R.: Symmetric 2-equilibria of unimodal voter distribution curves. Mimeo, Harvard University 1985
Eaton, B., Lipsey, R.: The principle of minimum product differentiation reconsidered: Some new developments in the theory of spatial competition. Rev. Econ. Stud. 42, 27–49 (1975)
Gale, D., Nikaido, H.: The Jacobian matrix and global univalence of mappings. Math. Ann. 159, 81–93 (1965)
Green, D., Palmquist, B., Schickler, E.: Partisan Hearts and Minds: Political Parties and the Social Identities of Voters. Yale University Press, New Haven 2002
Greenberg, J., Shepsle, K.: The effect of electoral rewards in multiparty competition with entry. Am. Pol. Sci. Rev. 81, 525–537 (1987)
Palfrey, T.: Spatial equilibrium with entry. Rev. Econ. Stud. 51, 139–156 (1984)
Parthasarathy, T.: On Global Univalence Theorems. Lecture Notes in Mathematics. Springer, Berlin Heidelberg New York 1983
Weber, S.: On hierarchical spatial competition. Rev. Econ. Stud. 59, 407–425 (1992)
Weber, S.: Entry deterrence in electoral spatial competition. Soc. Choice Welfare 15, 31–56 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Rubinchik, A., Weber, S. (2007). Existence and uniqueness of an equilibrium in a model of spatial electoral competition with entry. In: Kusuoka, S., Yamazaki, A. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 10. Springer, Tokyo. https://doi.org/10.1007/978-4-431-72761-3_6
Download citation
DOI: https://doi.org/10.1007/978-4-431-72761-3_6
Received:
Revised:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-72733-0
Online ISBN: 978-4-431-72761-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)