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Nash equilibrium in games with incomplete preferences

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  • Sophie Bade

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    Abstract

    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. Copyright Springer-Verlag Berlin/Heidelberg 2005

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    File URL: http://hdl.handle.net/10.1007/s00199-004-0541-1
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    Bibliographic Info

    Article provided by Springer in its journal Economic Theory.

    Volume (Year): 26 (2005)
    Issue (Month): 2 (08)
    Pages: 309-332

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    Handle: RePEc:spr:joecth:v:26:y:2005:i:2:p:309-332

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    Related research

    Keywords: Incomplete preferences; Nash equilibrium; multi-objective programming; Cournot Equilibrium.;

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    Cited by:
    1. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    2. Carlier, G. & Dana, R.-A., 2013. "Pareto optima and equilibria when preferences are incompletely known," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1606-1623.
    3. G. Carlier & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers 2014-060, Department of Research, Ipag Business School.
    4. Georgios Gerasimou, . "Dominance Solvable Games with Multiple Payoff Criteria," Discussion Paper Series, Department of Economics 201406, Department of Economics, University of St. Andrews.
    5. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    6. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
    7. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
    8. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, Center for Economic and Financial Research (CEFIR).
    9. repec:ipg:wpaper:59 is not listed on IDEAS

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