کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7367205 | 1479242 | 2018 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
No bullying! A playful proof of Brouwer's fixed-point theorem
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
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 us 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Economics - Volume 78, October 2018, Pages 1-5
Journal: Journal of Mathematical Economics - Volume 78, October 2018, Pages 1-5
نویسندگان
Henrik Petri, Mark Voorneveld,