A Statistically Robust Analysis of the N-Player Quantum Public Goods Game on a Calibrated Noise Model

This paper investigates the strategic implications of quantum mechanics on the N-Player Public Goods Game (PGG), a canonical model for the "Tragedy of the Commons."Classically, the PGG is dominated by a single, socially suboptimal Nash Equilibrium where all players 'defect' (free ride), leading to a collective loss. We investigate whether quantum strategies, specifically those that utilize multi-particle entanglement, can overcome this problem. We construct and evaluate three different strategies - a classical 'All Defect' benchmark, an 'Independent Quantum' strategy using superposition, and a 'Coordinated Quantum' strategy using an N-qubit entangled state - for N = 4 and N=5 player games and different pot multipliers (m = 1. 5, 2. 0). These techniques are run on a noise model calibrated to the IBM ibmq_manila quantum device, giving an honest estimate of performance on near-term hardware. Methodologically, we use repeated simulation for statistical robustness, reporting numbers with 95% confidence intervals. Our results exhibit a deep and statistically significant quantum benefit: the entangled approach systematically forms a cooperative Quantum Nash Equilibrium that achieves almost optimal payoffs, far surpassing the classical and independent quantum methods. Nevertheless, an extensive examination of the noise mechanisms at play shows that the scalability of this quantum solution is inherently limited in the Noisy Intermediate-Scale Quantum (NISQ) era. The interaction between error accumulation in the CNOT cascade needed for state preparation and the intrinsic decoherence of the entangled GHZ state produces an escalating failure mechanism that puts a bound on the realizable size of the game. This paper thereby offers both evidence of quantum advantage over a social dilemma and a realistic appraisal of the hardware-dictated constraints that will have to be overcome before such solutions are scalable.