Selected Topics In The Theory Of Fixed Points

We present a treatment for mathematical economists of three topics in the theory of xed points: (a) the Lefschetz xed point index; (b) the Lefschetz xed point theorem; (c) the theory of essential sets of xed points. Our treatment is geometric, based on elementary techniques, and largely selfcontained. In particular there is no essential reference to algebraic topology. Within the chosen scope of the paper the results are at the level of generality of the mathematical literature. The development of these theories for correspondences is emphasized. It emerges that the solution concepts of Kohlberg and Mertens (1986) have a de nite, though obscure, place in this theory.

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