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This PR adds Nash equilibrium existence (§33 of Knill's "Some Fundamental Theorems in Mathematics", the section's boxed main theorem) as a new eval problem: every finite n-player game in mixed strategies admits at least one Nash equilibrium. Mathlib has the standard simplex and finite-sum/product machinery but no game theory at all (no Mathlib/GameTheory/ module); no formalization of Nash equilibrium existence was found in any major proof assistant. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the Nash equilibrium existence theorem as a new lean-eval challenge problem — §33 of Oliver Knill's Some Fundamental Theorems in Mathematics (the section's boxed main theorem).
Every finite
n-player game in mixed strategies admits at least one Nash equilibrium.mathlib has
stdSimplex ℝ Sand the standard finite-sum/product machinery but no game theory at all — there is noMathlib/GameTheory/module, andgrep -ri nash,mixed.strategy,best.responsereturns nothing relevant. The Challenge ships four auxiliary definitions:MixedStrategy,StrategyProfile,expectedPayoff, andIsNashEquilibrium. A search found no formalization of Nash equilibrium existence in any major proof assistant.Companion PRs (also from §33): #286 Brouwer fixed-point and #287 Kakutani fixed-point — the two routes to a proof.
🤖 Prepared with Claude Code