of models created in various coalitions: $$\begin{split}
 & v(A) = 1, v(B) = 1, v(C) = 1
\\
 & v(A \cup B) = 2, v(A \cup C) = 2, v(B \cup C) = 2
 \\
 & v(A \cup B \cup C) = 3
\end{split}$$ A payoff vector $<x_A,x_B,x_C> = <1.5,1.5,1.5>$ would have been stable according to **Definition 1** because it is easily verifiable the sum of payoffs to any subset of players exceed the value created by them. However, in a modified game where resources created by a coalition can be duplicated for free, player $A$ and player $B$, for example, can choose to leave the grand coalition and work together to both earn a payoff of higher than 1.5 (Since they can pool their data together in subcoalition $A \cup B$ to potentially create a model of value 2 and earn a payoff $<x_A, x_B> =<2,2>$). Thus, the original definition of stability fails for our modified game.

We redefine, in an intuitive way, the definition of stability in a modified game:

In a modified game where the grand coalition $N$ of $n$ players forms, a payoff vector $<x_1,x_2,...,x_n>$ is **stable** if and only if for any subcoalitions $C \subseteq 