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arXiv · 2406.15795

Risk-Dominant Equilibrium in Quantum Prisoner's Dilemma

Ahmed S. Elgazzar
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Abstract

The choice of a unique Nash equilibrium (NE) is crucial in theoretical classical and quantum games. The Eiswer-Wilkens-Lewenstein quantization scheme solves the prisoner's dilemma only for high entanglement. At medium entanglement, there are multiple NEs. We investigate the selection of a unique NE in the quantum prisoner's dilemma with variable dilemma strength parameters. The risk-dominance criterion is used. The influence of the dilemma strength parameters and entanglement is emphasized. We found that entanglement completely controls the risk-dominant equilibrium. Entanglement promotes quantum-cooperation in the risk-dominant equilibrium and thus improves its outcome.

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Ahmed S. Elgazzar. 2024-06-22. Risk-Dominant Equilibrium in Quantum Prisoner's Dilemma. https://arxiv.org/abs/2406.15795

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