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Entanglement guarantees emergence of cooperation in quantum prisoner's dilemma games on networks.

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 √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 γ is less than the threshold arccos √b/b, then the equilibrium frequency of cooperations of the games is positively correlated to the entanglement degree γ, and that if γ is less than arccos √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.

SUBMITTER: Li A

PROVIDER: S-EPMC4155336 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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Project description:Across a variety of contexts, adults tend to cooperate more with ingroup members than outgroup members. However, humans belong to multiple social groups simultaneously and we know little about how this cross-categorization affects cooperative decision-making. Nationality and gender are two social categories that are ripe for exploration in this regard: They regularly intersect in the real world and we know that each affects cooperation in isolation. Here we explore two hypotheses concerning the effects of cross-categorization on cooperative decision-making. First, the additivity hypothesis (H1), which proposes that the effects of social categories are additive, suggesting that people will be most likely to cooperate with partners who are nationality and gender ingroup members. Second, the category dominance hypothesis (H2), which proposes that one category will outcompete the other in driving decision-making, suggesting that either nationality or gender information will be privileged in cooperative contexts. Secondarily, we test whether identification with-and implicit bias toward-nationality and gender categories predict decision-making. Indian and US Americans (N = 479), made decisions in two cooperative contexts-the Dictator and Prisoner's Dilemma Games-when paired with partners of all four social categories: Indian women and men, and US American women and men. Nationality exerted a stronger influence than gender: people shared and cooperated more with own-nationality partners and believed that own-nationality partners would be more cooperative. Both identification with-and implicit preferences for-own-nationality, led to more sharing in the Dictator Game. Our findings are most consistent with H2, suggesting that when presented simultaneously, nationality, but not gender, exerts an important influence on cooperative decision-making. Our study highlights the importance of testing cooperation in more realistic intergroup contexts, ones in which multiple social categories are in play.

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Entanglement guarantees emergence of cooperation in quantum prisoner's dilemma games on networks.

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