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From the KKM principle to the Nash Equilibria

Sehie Park


The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. A KKM space is an abstract convex space satisfying the partial KKM principle and its “open” version. In this paper, we clearly show that a sequence of statements from the partial KKM principle to the Nash equilibria can be obtained for any KKM spaces. This unifies previously known several proper examples of such sequences for particular types of KKM spaces.

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