  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.
