real life: business cooperation usually exists between only a few corporations. However, our paper considers it desirable for all players to cooperate and show that under certain optimality conditions, they will choose to do so.\
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Much analysis in cooperative games then focuses on what coalitions will form and how the resources generated in such coalitions can be divided amongst the participating players (termed as *outcomes* of the game). In the following sections, we will formally define such cooperative games [@10] and investigate how such definitions can be interpreted in the context of a multi-party machine learning process. Subsequently, we identify how conventional cooperative game concepts fail to represent the data sharing process adequately and suggest modifications.

Defining a cooperative game with a characteristic function
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Assume that $N$ represents a set of $n$ players. Define $v: 2^n \xrightarrow{} \mathcal{R}$ as a *characteristic function*. A *characteristic function* maps any coalition $C \subseteq N$, or a subset of players, to a real number which represents the value that is generated when this coalition of player chooses to work together.\
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In the context of multi-party machine learning, we can imagine that when players choose to work together (in the form of 