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Nash equilibrium in games with incomplete preferences

In: Rationality and Equilibrium

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  • Sophie Bade

    (New York University)

Abstract

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.

Suggested Citation

  • Sophie Bade, 2006. "Nash equilibrium in games with incomplete preferences," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 67-90, Springer.
    • Handle: RePEc:spr:steccp:978-3-540-29578-5_4
    DOI: 10.1007/3-540-29578-X_4
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