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| Entanglement Guarantees Emergence of Cooperation in Quantum Prisoner's Dilemma Games on Networks | |
| Li, Angsheng; Yong, Xi | |
| 2014 | |
| Source | SCIENTIFIC REPORTS
 |
| ISSN | 2045-2322 |
| Volume | 4 |
| English Abstract | It was known that cooperation of evolutionary prisoner's dilemma games fails to emerge in homogenous networks such as random graphs. Here we proposed a quantum prisoner's dilemma game. The game consists of two players, in which each player has three choices of strategy: cooperator (C), defector (D) and super cooperator (denoted by Q). We found that quantum entanglement guarantees emergence of a new cooperation, the super cooperation of the quantum prisoner's dilemma games, and that entanglement is the mechanism of guaranteed emergence of cooperation of evolutionary prisoner's dilemma games on networks. We showed that for a game with temptation b, there exists a threshold arccos root b/b for a measurement of entanglement, beyond which, (super) cooperation of evolutionary quantum prisoner's dilemma games is guaranteed to quickly emerge, giving rise to stochastic convergence of the cooperations, that if the entanglement degree gamma is less than the threshold arccos root b/b, then the equilibrium frequency of cooperations of the games is positively correlated to the entanglement degree gamma, and that if gamma is less than arccos root b/b and b is beyond some boundary, then the equilibrium frequency of cooperations of the games on random graphs decreases as the average degree of the graphs increases.; It was known that cooperation of evolutionary prisoner's dilemma games fails to emerge in homogenous networks such as random graphs. Here we proposed a quantum prisoner's dilemma game. The game consists of two players, in which each player has three choices of strategy: cooperator (C), defector (D) and super cooperator (denoted by Q). We found that quantum entanglement guarantees emergence of a new cooperation, the super cooperation of the quantum prisoner's dilemma games, and that entanglement is the mechanism of guaranteed emergence of cooperation of evolutionary prisoner's dilemma games on networks. We showed that for a game with temptation b, there exists a threshold arccos root b/b for a measurement of entanglement, beyond which, (super) cooperation of evolutionary quantum prisoner's dilemma games is guaranteed to quickly emerge, giving rise to stochastic convergence of the cooperations, that if the entanglement degree gamma is less than the threshold arccos root b/b, then the equilibrium frequency of cooperations of the games is positively correlated to the entanglement degree gamma, and that if gamma is less than arccos root b/b and b is beyond some boundary, then the equilibrium frequency of cooperations of the games on random graphs decreases as the average degree of the graphs increases. |
| Indexed Type | SCI |
| Department | [Li, Angsheng; Yong, Xi] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100864, Peoples R China. |
| Language | 英语 |
| WOS ID | WOS:000341447100003 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16822 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Li, Angsheng,Yong, Xi. Entanglement Guarantees Emergence of Cooperation in Quantum Prisoner's Dilemma Games on Networks[J]. SCIENTIFIC REPORTS,2014,4. |
| APA | Li, Angsheng,&Yong, Xi.(2014).Entanglement Guarantees Emergence of Cooperation in Quantum Prisoner's Dilemma Games on Networks.SCIENTIFIC REPORTS,4. |
| MLA | Li, Angsheng,et al."Entanglement Guarantees Emergence of Cooperation in Quantum Prisoner's Dilemma Games on Networks".SCIENTIFIC REPORTS 4(2014). |
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