Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking mechanistic interpretability. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. We validate the framework by demonstrating it rediscovers the optimal $[\![15,7,3]\!]$ quantum Hamming code (Calderbank-Shor-Steane 1996) from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges. Applied across six objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, and connectivity enhancement -- the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including $[\![100,50,4]\!]$ with distance-4 protection and 50\% encoding rate, with tractable $O(n^3)$ per-iteration complexity enabling discovery in under one hour. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.

Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational brute-force search lacking mechanistic interpretability. We introduce a game-theoretic framework that recasts code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. Applied to graph state stabilizer codes, the framework discovers codes across six distinct objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, and connectivity enhancement -- through objective reconfiguration rather than algorithm redesign. Game dynamics spontaneously generate a $[\![15,7,3]\!]$ code with bipartite cluster-state structure enabling measurement-based quantum computation while maintaining distance $d=3$, achieving 40\% overhead reduction versus surface codes at equivalent distance. Equilibrium analysis provides transparent mechanistic insights connecting strategic topology to code parameters, opening research avenues at the intersection of game theory, optimization, and quantum information.

Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking mechanistic interpretability. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. We validate the framework by demonstrating it rediscovers the optimal $[\![15,7,3]\!]$ quantum Hamming code (Calderbank-Shor-Steane 1996) from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges. Applied across six objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, and connectivity enhancement -- the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including $[\![100,50,4]\!]$ with distance-4 protection and 50\% encoding rate, with tractable $O(n^3)$ per-iteration complexity enabling discovery in under one hour. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.