Joe Ross will give the talk on Monday, November 15 at 4:15 in Math 528. This lecture will be open to all.
Abstract: For an exchange economy without production, Brouwer's fixed point theorem can be used to show the existence of an equilibrium vector of prices. We will use an algorithm related to Sperner's lemma to find fixed points of mappings of simplices into themselves. For an important class of games, Kakutani's fixed point theorem shows the existence of an equilibrium. We will discuss matrix games as a concrete example. We will also consider examples in which agents should misrepresent their preferences.
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