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Existence and Uniqueness of Nash Equilibrium in Electoral Competition Games: The Hybrid Case
Author(s) -
SAPORITI ALEJANDRO
Publication year - 2008
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/j.1467-9779.2008.00388.x
Subject(s) - contest , nash equilibrium , mathematical economics , economics , uniqueness , strategy , competition (biology) , stochastic game , best response , symmetric equilibrium , microeconomics , epsilon equilibrium , repeated game , game theory , equilibrium selection , mathematics , mathematical analysis , ecology , political science , law , biology
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, referred 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 does indeed exist.