A fixed point theorem for discontinuous functions

Herings, Jean-Jacques
(2008) Operations Research Letters — Vol. 36, n° 1, p. 89-93 (2008)

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  • Herings, Jean-JacquesUniversiteit Maastricht
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Abstract
Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.
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Herings, J.-J. (2008). A fixed point theorem for discontinuous functions. Operations Research Letters, 36(1), 89-93. https://doi.org/10.1016/j.orl.2007.03.008 (Original work published 2008)