الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
When it comes to global issues, interactions among participants are always asymmetric due to the availability of resources and environmental impacts. Thus, it is important to analyze decision-making among participants with different strategies. Therefore, we introduce the quantum prisoner’s dilemma in asymmetric strategy spaces. The formulation with two dilemma strength parameters is considered, and the Eisert–Wilkens–Lewenstein quantization scheme is applied. The properties of Nash equilibrium are examined for all possible cases of the values of the dilemma strength parameters and for each level of asymmetry. A solution to the dilemma can be obtained only in some extreme limits where the environmental influence is the largest. Consequently, it is unlikely to find a solution to the dilemma in the quantum domain with asymmetric strategy spaces. Therefore, strategies need to be standardized when dealing with global issues. The effect of the entanglement on the behavior of the quantum Prisoner’s Dilemma game is studied in detail. We have extended the investigation to cover the whole range of entanglement, to study the symmetry of the quantum Prisoner’s Dilemma game with respect to the entanglement.
The emergence of cooperation in the thermodynamic limit of social dilemma is an emerging field of research. A particularly analytical approach is to utilize a mapping between the spin 1/2 Ising model in 1D and the social dilemma game and calculate the magnetization. The Ising model is a model of ferromagnetism that describes the phase transition in magnetics. It has many applications in magnetism, neuroscience and spin glasses. We investigate the behavior of the participants in the prisoner’s dilemma game in the thermodynamic limit. Then, we study the influence of the two dilemma strength parameters of the rescaled prisoner’s dilemma on the behavior of the participants in the thermodynamic limit. Increment the gamble-intending parameter is found to promote cooperation at low temperature values. While increment the risk-averting parameter is found to promote defection in both classical and quantum versions of the rescaled prisoner’s dilemma.