Collective choice rules and collective rationality: a unified method of characterizations

To analyze the willingness to cooperate of farmers to participate in water management, we base on game theory and first carry on single static game analysis of willingness to cooperate for farmers to participate in water management, and find that farmers are into a Prisoners Dilemma in a single game, individual rationality comes into conflict with collective rationality, at this time farmers have a tendency to "free riders", so it is difficult to achieve cooperation between the farmers. Then trying to break the prisoners' dilemma, we carry on the farmers repeated dynamic game, the analysis is carried on in the context of incomplete information and limited rationality, we carry on game evolution analysis for willingness to cooperate for farmers to participate in water management. In order to guarantee the rationality of the study, we conduct a survey of willingness to cooperate of farmers to participate in water management in province of Zhejiang and finally confirm that the study is reasonable. And through the analysis of the full text, we conclude six important conclusions.

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A nonlocal game for witnessing quantum networks

npj Quantum Information ◽

10.1038/s41534-019-0203-6 ◽

2019 ◽

Vol 5 (1) ◽

Cited By ~ 3

Author(s):

Ming-Xing Luo

Keyword(s):

Computational Complexity ◽

Main Idea ◽

Bell Inequalities ◽

Theoretical Computer Science ◽

Graph Representation ◽

Necessary Condition ◽

Quantum Networks ◽

Theoretical Computer ◽

Sufficient And Necessary Condition ◽

Unified Method

Abstract Nonlocal game as a witness of the nonlocality of entanglement is of fundamental importance in various fields. The well-known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks consisting of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We propose an efficient method to construct multipartite nonlocal games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply a linear Bell testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond CHSH game. These results have interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.

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