This paper deals with the problem of fairly allocating a certain amount of benefit among individuals or organizations with multiple criteria for their performance evaluation. It is an extension work of our paper on game theoretic approaches to weight assignments in data envelopment analysis (DEA) problems (Sekine et al., 2014). One of the main conclusions in our previous work is that the core of the TU (transferable utility) DEA game is non-empty if and only if the game is inessential, that is, the evaluation indices are identical for all the criteria for each player. This condition is equivalent to a trivial single-criterion setting, which motivates us to turn to the NTU (non-transferable utility) situation and check the existence of the fractional solutions. In this study, we contribute on showing the existence of α-core, and giving two sufficient conditions such that β-core exists and is identical to α-core in NTU DEA game. Our discussion is also interesting in light of a direction to improve the robustness of the β-core existence condition by relaxing the inessential condition in TU DEA game.
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