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Nash equilibrium in games with incomplete preferences

  • Sophie Bade
Conference paper
Part of the Studies in Economic Theory book series (ECON.THEORY, volume 26)

Summary

This paper investigates Nash equilibrium under the possibility that preferences may be incomplete. I characterize the Nash-equilibrium-set of such a game as the union of the Nash-equilibrium-sets of certain derived games with complete preferences. These games with complete preferences can be derived from the original game by a simple linear procedure, provided that preferences admit a concave vector-representation. These theorems extend some results on finite games by Shapley and Aumann. The applicability of the theoretical results is illustrated with examples from oligopolistic theory, where firms are modelled to aim at maximizing both profits and sales (and thus have multiple objectives). Mixed strategy and trembling hand perfect equilibria are also discussed.

Keywords and Phrases

Incomplete preferences Nash equilibrium multiobjective programming Cournot Equilibrium 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sophie Bade
    • 1
  1. 1.New York UniversityNew YorkUSA

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