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On a parameterized system of nonlinear equations with economic applications
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On a parameterized system of nonlinear equations with economic applications

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  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

  • Yang, Z.F.

Abstract

We study a parameterized system of nonlinear equations. Given a nonempty, compact, and convex set, an affine function, and a point-to-set mapping from the set to the Euclidean space containing the set, we constructively prove that, under certain (boundary) conditions on the mapping, there exists a connected set of zero points of the mapping, i.e., the origin is an element of the image for every point in the connected set, such that the connected set has a nonempty intersection with both the face at which the affine function is minimized and the face at which that function is maximized. This result generalizes and unifies several well-known existence theorems including Browder’s fixed point theorem and Ky Fan’s coincidence theorem. An economic application with constrained equilibria is also discussed.
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Suggested Citation

  • Talman, A.J.J. & Yang, Z.F., 2012. "On a parameterized system of nonlinear equations with economic applications," Other publications TiSEM 8233343d-0b60-428d-a20b-6, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:8233343d-0b60-428d-a20b-6bcefbc8542f
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