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Chinese Physics Letters

Impact of Distribution Fairness Degree and Entanglement Degree on Cooperation

Xin Bing Zhao, Boyang Liu, Ying Yi, Hong‐Yi Dai, Ming Zhang

Published Mar 1, 2018• 1 citation
Publisher

Abstract

We explore the impact of distributional fairness degree and entanglement degree on the cooperation between different players by investigating a modified prisoner's dilemma game. We not only introduce a new concept of distributional fairness degree, but also obtain the cooperation conditions for overcoming dilemma in terms of fairness and entanglement inequalities. It is demonstrated that distributional fairness can be of fundamental importance to promote cooperation with the help of quantum entanglement.

DOI
10.1088/0256-307x/35/3/030202

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We explore the impact of distributional fairness degree and entanglement degree on the cooperation between different players by investigating a modified prisoner's dilemma game. We not only introduce a new concept of distributional fairness degree, but also obtain the cooperation conditions for overcoming dilemma in terms of fairness and entanglement inequalities. It is demonstrated that distributional fairness can be of fundamental importance to promote cooperation with the help of quantum entanglement.
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The motivation of this talk is to investigate what quantum resources will bring about in our daily life. A kind of quantization for general bipartite games is first given and then applied to both the modified classical “cash in a hat” game and modified Prisoners Dilemma game with different distribution policies. It is shown that quantum entanglement can bring full cooperation with the help of fair distribution policies. It is further demonstrated that quantum networks will make possible playing quantum game between remote players. Two schemes are given to illustrate how to play distributed quantum games between two players on the nodes of quantum networks. In our opinion, it is a worthy research topic to investigate how quantum entanglement can be exploited to achieve full cooperation with equitable distribution polices.
Cooperation is a fundamental aspect of biological systems and human society. In this work, we propose a generalized prisoner's dilemma quantum game and study the game on Watts-Strogatz small-world network (WS model) with different values of entanglement. Here entanglement is used as a metaphor to study relationship between players. In a single step, each player has three strategies to choose: cooperation, defection and adopting a special quantum strategy first introduced by Eisert (denoted by Q). The person who chooses the quantum strategy Q can be regarded as a super cooperator. In prisoner's dilemma game, cooperation is very hard to emerge on relatively homogeneous networks, such as random graphs and WS model. Our experimental results show that in generalized prisoners dilemma quantum game, entanglement can guarantee emergence of super cooperators and greatly increase the payoff of the whole network. Even on homogeneous networks with very large inducement value(b is close to 2), the frequency of cooperators can still exceeds 70%. This work provides a new insight into understanding cooperation when considering the role of relationship between cooperators.