data sharing) to create a model from the pooled data, this model represents the value created by a coalition of players; the characteristic function $v(.)$ can be certain statistical or information-centric metric used to indicate the value of such models. Furthermore, one can even use the model’s performance over a test data set as an indicator of its value.

In fact, various analyses in this paper make no assumptions of the exact characteristic function used in a data sharing process. However, towards the end of the paper, we justify the use of certain functions over others. As we will see from experiments in section 9, there are many different interpretations of characteristic functions and they lead to different outcomes.

### Outcomes of cooperative games

An *outcome* of a cooperative game with $n$ players and a given characteristic function $v(.)$ is characterised entirely by the following two parts:

1.  a partition of players into different coalitions, called a *coalition structure*; and

2.  a *payoff vector* $<x_1,...,x_n>$, which distributes the value of each coalition among its members $\sum_{i\in C} x_i \leq v(C)$ for all coalition $C$ formed in the *coalition structure*.

The first part tells us which coalitions will be formed; the 