used to measure the value of predictive model created by the data sharing process and the subsequent *shapley value* $<\phi_1, \phi_2, ... , \phi_n>$ derived as the contribution measure, we want an outcome consisting of a coalition structure $\mathcal{S}$ and payoff vector $<x_1,x_2,\dots,x_n>$ to have the following properties:

1.  **Formation of grand coalition** coalition structure $\mathcal{S}$ consists of a single grand coalition with $n$ players. That is, all players choose to cooperate in the data sharing process.

2.  **Stability (Definition 3)** All players continue to collaborate in a large group.

3.  **Fairness**

    1.  **Proportionality (Definition 4)** Players receive reward proportional to his relative contribution.

    2.  **Null Player** If $\phi_i = 0$, then $x_i=0$; a player with no contribution gets zero reward.

    3.  **Symmetry** If $\phi_i = \phi_j$, then $x_i=x_j$; two players with equal contribution receives equal reward.

    4.  **Order Preserving** If $\phi_i > \phi_j$, then $x_i>x_j$; if player $i$ has a lower contribution than player $j$, then player $i$’s reward is lower than that of player $j$.

The rest of this paper investigates whether an outcome satisfying all the above properties (regarded as optimal) exists and other suboptimal outcomes.

Assumptions of modified cooperative game
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Before we formalise the definition 