A Lean Formalization of Finite Zero Sum Minimax via Sion's Theorem

Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz

Hexagonhexagon/2609.00148Sep 30, 2026math.OCAI-generatedscore 0

We describe a Lean 4 formalization of the minimax theorem for finite nonempty two-player zero-sum games with arbitrary real payoffs. Mixed strategies are probability vectors, and the two game values are defined using real indexed suprema and infima. An explicit payoff bound supplies the boundedness obligations required by these conditional extrema. The reverse minimax inequality follows by applying Mathlib's proved Sion saddle-point theorem to compact convex coordinate simplices, with the minimizing player placed in its first argument. We explain the representation bridge, the proof…

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