Scandinavian Working Papers in Economics
HomeAboutSeriesSubject/JEL codesAdvanced Search
Stockholm School of Economics SSE Working Paper Series in Economics, Stockholm School of Economics

No 2016:3:
No bullying! A playful proof of Brouwer's fixed-point theorem

Henrik Petri () and Mark Voorneveld ()

Abstract: We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of n-dimensional Euclidean space has a convergent subsequence with a limit in that set. Our main tool is a `no-bullying' lemma for agents with preferences over indivisible goods. What does this lemma claim? Consider a finite number of children, each with a single indivisible good (a toy) and preferences over those toys. Let's say that a group of children, possibly after exchanging toys, could bully some poor kid if all group members find their own current toy better than the toy of this victim. The no-bullying lemma asserts that some group S of children can redistribute their toys among themselves in such a way that all members of S get their favorite toy from S, but they cannot bully anyone.

Keywords: Brouwer; fixed point; indivisible goods; KKM lemma; (follow links to similar papers)

JEL-Codes: C62; C63; C69; D51; (follow links to similar papers)

9 pages, April 16, 2016, Revised June 20, 2017

Before downloading any of the electronic versions below you should read our statement on copyright.
Download GhostScript for viewing Postscript files and the Acrobat Reader for viewing and printing pdf files.

Full text versions of the paper:

hastec2016_003.pdf    PDF-file (262kB) 
Download Statistics

Questions (including download problems) about the papers in this series should be directed to Helena Lundin ()
Report other problems with accessing this service to Sune Karlsson () or Helena Lundin ().

Programing by
Design by Joachim Ekebom

Handle: RePEc:hhs:hastec:2016_003 This page was generated on 2017-06-20 14:22:18