2021-01-28: Jérémy Ledent (MSP)

Sat, 21 Oct 2023 21:24:08 +0100

Jérémy Ledent (MSP)

Combinatorics, Topology and Game theory: a proof of Nash's theorem

Abstract

The aim of this talk is to state and prove Nash's theorem, which says that every finite game with mixed strategies has a Nash equilibrium. The proof makes use of two other famous results: Sperner's lemma, a combinatorial result about coloring the vertices of a triangulation, and Brouwer's fixed-point theorem. Thus, my talk will be organised into three largely independent parts: first I will sketch the proof of Sperner's lemma; then I will use Sperner's lemma to prove Brouwer's theorem; and finally I will use Brouwer's theorem to prove the existence of Nash equilibria.

2021-01-28 15:00:00 UTC
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