Bridging Theory and Practice in Quantum Game Theory: Optimized Implementation of the Battle of the Sexes with Error Mitigation on NISQ Hardware
Bibliographic record
Abstract
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 advan-tages 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 decisionmaking systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".