of a real-life data-sharing process, imagine $n$ data providers come together to create a predictive model from the pooled data. Then using a monotonic characteristic function $v(.)$ to measure the value of the predictive model, we are able to derive the relative contributions of the players with the *Shapley value*. Subsequently, an optimal outcomes corresponds to a reward payoff for the players such that they have no incentives to break away from the grand coalition and the reward also commensurates each player’s relative contribution. In this section, we investigate how we can find this optimal outcome efficiently.\
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We consider an outcome to a modified game *optimal* if they satisfy all properties in the Section 5. Hence, the task of finding an optimal outcome becomes one of finding the feasible region of the division of rewards to the players $<x_1,x_2,\dots,x_n>$ such that all desirable properties are satisfied. However, this is computationally inefficient because the definition of stability alone implies that we need to check $2^n$ constraints. Fortunately, we show, in the following proposition, that the set of stable solution payoffs can be found by checking only $n$ constraints, given that the characteristic function $v(.)$ is monotonic.

**Stable Solution Set** Given 