any player. To do this, we need to redefine what a *payoff vector* is.

In a modified game, a **payoff vector** $<x_1,x_2,...,x_n>$ to a coalition structure is such that for all coalitions $C$ belonging to the coalition structure formed, $x_i \leq v(C)$ for any player $i \in C$.

Compared to the definition of *payoff vector* in Section 3.1.1, this new definition restricts the payment to a coalition of players such that each player cannot receive more than the value created in this coalition. Notice this is different from conventional cooperative games, which dictate that the sum of payments received by all the players cannot exceed the value created in a coalition.

The data sharing process can now be represented entirely by this modified game with a new definition of *payoff vector* in an outcome. However, changing this single definition leads to a myriad of effects on the concept of stability, fairness and outcome, which will be covered in the subsequent sections.

Alternative definition of stability
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Under this modified game, the original definition of stability (**Definition 1**) no longer ensures that a payoff vector is stable. For example, for a three-player game with the following characteristic function defining the value 