Abstract
Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner’s dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner’s dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner’s dilemma is greatly impacted by the combined effect of entanglement and coupling.
Highlights
Evolutionary games on multilayer networks are attracting growing interest
In accordance with common practice[8], the temptation of defection T = b determines the payoff received by a defector when meeting a cooperator, the reward for mutual cooperation is R = 1, the punishment for mutual defection is defined by P = 0, and the sucker’s payoff S = 0 is the payoff received by a cooperator if meeting a defector, where 1 < b < 2
We first investigate a special case of γ = 0 in which there dose not exist quantum entanglement so that the quantum prisoner’s dilemma (QPD) degenerates to classical prisoner’s dilemma (PD), and the evolution on networks G1 and G2 is mainly affected by coupling factor α
Summary
Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. The impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Evolutionary games on networks can be classified into two categories based on the located interaction structure: evolutionary games on simplex networks, and games on multilayer networks, respectively The former mainly include scale-free networks[41], small world networks[42], etc. Among previous studies of coupled network games, game models are almost classical version where the quantum entanglement, representing an underlying connection among individuals, is not taken into consideration. The QPD, including three strategies cooperation (C), defection (D), and super cooperation (Q), is used to model the interaction in quantum world which is located on another network. We mainly study the impact of α and γ on the co-evolution of PD and QPD on the coupled networks
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