A Generalization of Brouwer's Fixed Point Theorem.¶
Kakutani, S. (1941). A Generalization of Brouwer's Fixed Point Theorem. Duke Mathematical Journal, 8(3), 457-459.
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Primes¶
- Fixed Point
- Existence is certified structurally rather than by guesswork: the best-response map is continuous on a convex compact strategy set, so the relevant fixed-point theorem guarantees an equilibrium exists before it is located — the same certification an economist invokes when proving general-equilibrium existence.
This sourceKakutani fixed-point theorem for set-valued maps on convex compact sets — the existence tool invoked for equilibria of best-response correspondences in economics.
- Existence is certified structurally rather than by guesswork: the best-response map is continuous on a convex compact strategy set, so the relevant fixed-point theorem guarantees an equilibrium exists before it is located — the same certification an economist invokes when proving general-equilibrium existence.
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