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Existence of Equilibrium in Generalized Games with Abstract Convexity Structure

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  • J. V. Llinares

    (Universidad de Murcia)

Abstract

The aim of this paper is to prove the existence of equilibrium for generalized games or abstract economies in contexts where the convexity conditions on strategy spaces and preference correspondences are relaxed and an arbitrary number of agents is considered. The results are based on a fixed-point theorem in which the convexity condition on sets and images of correspondences is replaced by a general notion of abstract convexity, called mc-spaces, generalizing the notions of simplicial convexity, H-spaces, and G-convex spaces.

Suggested Citation

  • J. V. Llinares, 2000. "Existence of Equilibrium in Generalized Games with Abstract Convexity Structure," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 149-160, April.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:1:d:10.1023_a:1004618113022
    DOI: 10.1023/A:1004618113022
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    References listed on IDEAS

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    1. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    2. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    3. Tarafdar, E., 1991. "A fixed point theorem and equilibrium point of an abstract economy," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 211-218.
    4. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    5. Llinarès, Juan Vicente, 1998. "Abstract convexity, some relations and applications," CEPREMAP Working Papers (Couverture Orange) 9803, CEPREMAP.
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