Graph continuous function: Difference between revisions

Revision as of 09:39, 24 May 2009

Revision as of 10:06, 15 August 2009

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The property is interesting in view of the following theorem.

If, for <math>1\leq i\leq N</math>, <math>A_i\subseteq\Bbb{R}^m</math> is non-empty, [[convex]], and [[compact set|compact]]; and if <math>U_i:A\longrightarrow\Bbb{R}</math> is [[quasi-concave function|quasi-concave]] in <math>a_i</math>, [[upper semi-continuous]] in <math>\mathbf{a}</math>, and graph continuous, then the game <math>[(A_i,U_i); i=1,\ldots,N]</math> possesses a [[pure strategy]] [[Nash equilibrium]].

==References==