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1·The Bondareva-Shapley theorem:The core of the game is non-empty if and only if the game is balanced (Bondareva 1963, Shapley 1967).

Bondareva-Shapley定理：只有而且仅有当博弈是平衡的时候，中心才非空。

2·This particular planetary nebula, pictured above and designated Shapley 1 after the famous astronomer Harlow Shapley, has a very apparent annular ring like structure.

上图中的行星状星云叫做Shapley 1以著名天文学家Harlow Shapley的名字命名，它有非常明显的环状结构。

3·Finally, it USES Shapley value method to explore the optimum ratio of the energy saving benefits distribution in cooperative game and puts forward corresponding Suggestions.

运用shapley值法探讨合作博弈中的节能效益分配最佳比例，并提出相应的建议。

4·Mr Roth, who won the prize jointly with Lloyd Shapley in 2012, found that the structure of matching markets made a significant difference in determining who wound up with whom.

曾在2012年与劳埃德·沙普利分享诺奖的罗斯发现，配对市场的结构会在决定谁与谁配对方面产生明显的差异。

5·The applicability of third-part test process is illustrated as Bayesian Nash Equilibrium of the compound strategies game model, and a discussion on cooperation possibility is made with Shapley value.

通过混合策略的贝叶斯纳什均衡给出第三方测试过程适用条件，采用沙普利值对参与方合作可能性进行探讨。