Palanivel

Palanivel R

Abstract Supply chains face increasingly frequent and severe disruptions, while the strategic interactions among suppliers, manufacturers, logistics providers and retailers are traditionally modelled with classical, non-cooperative game theory that struggles to capture correlated, non-classical strategic correlations and scales poorly on the combinatorial optimization problems that resilience investment decisions induce. This paper proposes an integrated \emph{Quantum Game-Theoretic Optimization} framework for resilient supply chains under AI-driven disruption management. The framework combines (i) an Eisert--Wilkens--Lewenstein (EWL) quantum game formulation of the four-agent resilience-investment game, (ii) a Quantum Approximate Optimization Algorithm (QAOA) solver for the resulting resilience-allocation QUBO, augmented with a novel \emph{Ramanujan-inspired regularization} term built from the Hardy--Ramanujan partition asymptotic and Ramanujan summation (zeta-regularization), and (iii) a multi-agent reinforcement learning (MARL) layer whose learning-rate schedule is modulated by the Rogers--Ramanujan continued fraction. We formally derive the entangled state evolution, the Ising/QUBO mapping, the QAOA cost and mixer Hamiltonians, the Ramanujan regularization term, and the MARL update rule, and we present a five-layer reference system architecture. Using exact statevector simulation (no physical quantum hardware required), we address five research questions spanning equilibrium payoffs under entanglement, QAOA depth scaling, the effect of Ramanujan regularization on optimization-landscape stability, MARL performance under varying disruption severity, and an overall multi-metric benchmark against classical game theory, classical mixed-integer programming, and classical MARL baselines. Simulation results show that entanglement can raise total equilibrium payoff substantially above the classical (product-state) Nash equilibrium by escaping mutually-defecting ''no-investment'' traps, that QAOA approximation ratio improves with circuit depth up to a problem-dependent saturation point, that Ramanujan regularization yields a smoother but instance-dependent optimization landscape, and that the integrated framework achieves the highest service level and robustness score among five compared methods, at a moderate convergence-time cost. Complete derivations, a reproducible open-source Python implementation, and all simulation data are provided.