2 citations · 4 across the 6 of their papers we have counts for
6 papers
Von Neumann's minimax theorem through Fourier-Motzkin elimination
Mark Voorneveld
Fourier-Motzkin elimination, a standard method for solving systems of linear inequalities, leads to an elementary, short, and self-contained proof of von Neumann's minimax theorem.
On Smithson's fixed point theorem for order preserving multifunctions
Haruki Kono, Mark Voorneveld
Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains err…
No bullying! A playful proof of Brouwer's fixed-point theorem
Henrik Petri, Mark Voorneveld
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…
An elementary direct proof that the Knaster-Kuratowski-Mazurkiewicz lemma implies Sperner's lemma
Mark Voorneveld
Three central results in economic theory --- Brouwer's fixed-point theorem, Sperner's lemma, and the Knaster-Kuratowski-Mazurkiewicz (KKM) lemma --- are known to be equivalent. In…
Berge's Maximum Theorem for Noncompact Image Sets
Eugene A. Feinberg, Pavlo O. Kasyanov, Mark Voorneveld
This note generalizes Berge's maximum theorem to noncompact image sets. It is also clarifies the results from E.A. Feinberg, P.O. Kasyanov, N.V. Zadoianchuk, "Berge's theorem for n…
Congestion, equilibrium and learning: The minority game
Willemien Kets, Mark Voorneveld
The minority game is a simple congestion game in which the players' main goal is to choose among two options the one that is adopted by the smallest number of players. We character…