The Observer’s Dilemma:

Rick P. Trebino

Ahmed S. Elgazzar

A quantized version of the prisoner’s dilemma game based on the Marinatto–Weber quantization scheme is introduced. A four-qubit-basis initial entangled quantum state is assumed. Two domains for Nash equilibria are observed in terms of the degree of entanglement of the game. Each Nash equilibrium point is found to be Pareto optimal in its corresponding domain. Therefore, there is a unique solution to the game dilemma in each domain of the entanglement parameter. The maximally entangled limit is studied, and the players’ payoffs are found to equal the average of the payoff matrix independently of their choices. Consequently, any combination of players’ choices is a solution to the dilemma of the game. The nonentangled limits are also studied and found to coincide with the classical mixed-strategy game. Our results are equivalent to those of the noisy schemes of the quantum prisoner’s dilemma game. In our scheme, entanglement can be interpreted as a noise.

Wanda Strauven

Şahin Kaya Özdemir, Junichi Shimamura, Fumiaki Morikoshi +1 more

Effects of classical/quantum correlations and operations in game theory are analyzed using Samaritan's Dilemma. We observe that introducing either quantum or classical correlations to the game results in the emergence of a unique or multiple Nash equilibria (NE) which do not exist in the original classical game. It is shown that the strategies creating the NE and the amount of payoffs the players receive at these NE's depend on the type of the correlation. We also discuss whether the Samaritan can resolve the dilemma acting unilaterally.