夏普利值(Shapley value)與核仁(nucleolus)是合作對局論中兩個重要的解。本篇論文想研究的是，什麼情況下這兩個解會相等。
若一個對局的夏普利值與核仁相等，則我們稱這個對局滿足重合特性(coincidence property)。一個重合區域(coincidence region) 是指由ㄧ些滿足重合特性的對局所形成的凸錐體。在這篇論文裡我們提出了兩種造出重合區域方法。第ㄧ種方法造出了許多重合區域，我們稱為BP region。每ㄧ個BP region裡的對局稱為BP game。就我們所知，在文獻上所談到的所有滿足重合特性的對局都是BP game。我們也研究了BP region的數學性質，諸如兩個BP region相等的充分必要條件、一個BP region是MBP region (MBP region是指不會嚴格包含於任一個BP region的BP region) 的充分必要條件等等。
然而，既使只考慮三人對局，滿足重合特性的對局也不一定是BP game。因此，我們把BP region的想法一般化，得到一種方法來造出重合區域。這些重合區域就稱為BT region。我們證明了每一個BP region都是BT region，也證明所有滿足重合特性的三人對局必定在某個BT region裡。最後，我們提供一個滿足重合特性的四人對局，說明它不在任何一個BT region裡。

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