CS 294 - 1 Algorithmic Aspects of Game Theory Spring 2001 Lecture 2 : January 23

نویسنده

  • Christos Papadimitriou
چکیده

We begin by looking at a set of theorems from various disciplines and how they relate to one another. From combinatorics, we take Sperner’s Lemma which we can use to prove Brouwer’s Fixed Point Theorem from topology. Brouwer’s Fixed Point Theorem can be used to prove the Arrow-Debreu Theorem from economics which states that general equilibria exist, and can also be used to prove Kakutani’s Fixed Point Theorem. Kakutani’s Fixed Point Theorem can be used to prove that Nash Equilibria exist for all games. A graph illustrating how these theorems can be used to prove each other is given in Figure 2.1.

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تاریخ انتشار 2012