Bridging Theory and Practice in Quantum Game Theory: Optimized
  Implementation of the Battle of the Sexes with Error Mitigation on NISQ
  Hardware
Authors: name: Germán Díaz Agreda, name: Carlos Andres Duran Paredes, name: Mateo Buenaventura Samboni, name: Jhon Alejandro Andrade, name: Sebastián Andrés Cajas Ordoñez

Implementing quantum game theory on real hardware is challenging due to
noise, decoherence, and limited qubit connectivity, yet such demonstrations are
essential to validate theoretical predictions. We present one of the first full
experimental realizations of the Battle of the Sexes game under the
Eisert-Wilkens-Lewenstein (EWL) framework on IBM Quantum's ibm sherbrooke
superconducting processor. Four quantum strategies (I, H, R(pi/4), R(pi))
were evaluated across 31 entanglement values gamma in [0, pi] using 2048
shots per configuration, enabling a direct comparison between analytical
predictions and hardware execution. To mitigate noise and variability, we
introduce a Guided Circuit Mapping (GCM) method that dynamically selects qubit
pairs and optimizes routing based on real-time topology and calibration data.
The analytical model forecasts up to 108% payoff improvement over the
classical equilibrium, and despite hardware-induced deviations, experimental
results with GCM preserve the expected payoff trends within 3.5%-12%
relative error. These findings show that quantum advantages in strategic
coordination can persist under realistic NISQ conditions, providing a pathway
toward practical applications of quantum game theory in multi-agent, economic,
and distributed decision-making systems.