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Nash equilibrium in games with incomplete preferences

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Rationality and Equilibrium

Part of the book series: Studies in Economic Theory ((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.

I would like to thank Jean-Pierre Benôit, Juan Dubra, Alejandrio Jofre, Debraj Ray, Kim-Sau Chung and the seminar participants at NYU and at the Universidad de Chile for their comments. I am most grateful to Efe Ok, for his comments, criticism, suggestions and questions.

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Author information

Authors and Affiliations

  1. New York University, 269 Mercer street, 7th floor, New York, NY, 10003, USA

    Sophie Bade

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  1. Sophie Bade
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Editor information

Editors and Affiliations

  1. Krannert School of Management Department of Economics, Purdue University, West Lafayette, IN, 47907-2076, USA

    Charalambos D. Aliprantis  & James C. Moore  & 

  2. Department of Economics, Northwestern University, Evanston, IL, 60208, USA

    Rosa L. Matzkin

  3. Department of Economics, University of California, Berkeley, CA, 94720-3880, USA

    Daniel L. McFadden

  4. Department of Economics, University of Illinois, Champaign, IL, 61820, USA

    Nicholas C. Yannelis

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Bade, S. (2006). Nash equilibrium in games with incomplete preferences. In: Aliprantis, C.D., Matzkin, R.L., McFadden, D.L., Moore, J.C., Yannelis, N.C. (eds) Rationality and Equilibrium. Studies in Economic Theory, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29578-X_4

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  • DOI: https://doi.org/10.1007/3-540-29578-X_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29577-8

  • Online ISBN: 978-3-540-29578-5

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