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Multidimensional Political Competition with Non-Common Beliefs

  • Kazuya Kikuchi
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    This paper extends a probabilistic voting model with a multidimensional policy space, allowing candidates to have different prior probability distributions of the distribution of voters' ideal policies. In this model, we show that a platform pair is a Nash equilibrium if and only if both candidates choose a common generalized median of expected ideal policies. Thus, the existence of a Nash equilibrium requires not only that each candidate's belief have an expected generalized median, which is already a knife-edge condition, but also that the two medians coincide. We also study limits of ε-equilibria of Radner (1980) as ε → 0, which we call "limit equilibria." Limit equilibria are policy pairs that approximate choices by the candidates who almost perfectly optimize. We show that a policy pair is a limit equilibrium if and only if both candidates choose the same policy around which they form "opposite expectations" in a certain sense. For a limit equilibrium to exist (equivalently, for ε-equilibria to exist for all ε > 0), it is sufficient, though not necessary, that either candidate has an expected generalized median.

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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-226.pdf
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    Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd11-226.

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    Date of creation: Feb 2012
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    Handle: RePEc:hst:ghsdps:gd11-226
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    1. Radzik, Tadeusz, 1991. "Pure-strategy [epsiv]-Nash equilibrium in two-person non-zero-sum games," Games and Economic Behavior, Elsevier, vol. 3(3), pages 356-367, August.
    2. John Duggan, 2003. "Electoral Competition with Privately Informed Candidates," Theory workshop papers 505798000000000029, UCLA Department of Economics.
    3. Ziad, Abderrahmane, 1997. "Pure-Strategy [epsiv]-Nash Equilibrium inn-Person Nonzero-Sum Discontinuous Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 238-249, August.
    4. Carmona, Guilherme, 2010. "Polytopes and the existence of approximate equilibria in discontinuous games," Games and Economic Behavior, Elsevier, vol. 68(1), pages 381-388, January.
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