machine learning, this property is desirable because it encourages players to share data in a larger coalition to create a unified model instead of breaking off into smaller groups.

Let $<x_1,x_2,...,x_n>$ be a payoff vector to players [1,2,...,n]{}. Then this payoff vector is **stable** if and only if $\sum_{i \in C} x_i \geq v(C)$ for all $C \subseteq N$.

Intuitively, an outcome is stable if the reward received by each player at the end is such that no subset of players can simultaneously break off into smaller sub-coalitions which generate higher rewards than the sum of payment each player earns from the current reward. As the name suggests, one can interpret stability as some kind of equilibrium for the players, where there is no incentive for anyone to take deviating actions.

In conventional cooperative games, the set of all **stable** solution payoffs is called the $\textbf{Core}$. Notice that deriving the stable set of solution consists of finding the feasible region satisfying $2^n$ constraints (by **Definition 1**). Hence, the **Core** does not necessarily exist.

### Shapley value

On the other hand, when we divide the value created in the grand coalition $N$ to the participating players in a payoff vector, we 