Existence of equilibrium actions and of equilibrium : A note on the ‘new’ existence theorems |
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Authors: | Anders Borglin |
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Institution: | University of Lund, Lund, Sweden;University of Copenhagen, Copenhagen, Denmark |
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Abstract: | A lemma by Ky Fan, which asserts the existence of a maximal element relative to some ordering (an equilibrium action) in a compact choice set, is extended to a larger class of orderings. This extension allows one to generalize slightly several existence theorems and seems to be useful for the applications. Kakutani's fixed-point theorem and the existence of an equilibrium in a generalized game are used to exemplify this. In the last case the method of proof may be of some independent interest involving, as it does, the reduction of an n-person game to a corresponding 1-person game. |
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