🤖 AI Summary
Von Neumann’s minimax theorem—foundational to game theory and optimization—has traditionally been proven using functional analysis or fixed-point theorems, imposing high conceptual barriers.
Method: This paper provides the first direct, elementary, and self-contained proof based entirely on Fourier–Motzkin elimination (FME), employing only linear algebra and linear inequality reasoning. By integrating systematic variable elimination with convex separation principles, the proof constructs an explicit, rigorous derivation within two pages.
Contribution/Results: The approach significantly lowers pedagogical and conceptual thresholds, offering a transparent, accessible alternative for teaching and research in game theory and optimization. It demonstrates that classical elimination techniques—long overlooked in foundational proofs—possess untapped power for establishing core mathematical results, thereby revitalizing FME as a tool for elementary yet rigorous theorem proving.
📝 Abstract
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.