second part tells us that for each coalition formed in the first part, how value created in this coalition is divided amongst the players in it. In particular, we notice that second part implies that the sum of payoff distributed to members of a coalition cannot exceed the value generated by this coalition; for example, when a group of firms work together to generate some profits, the payment given to all the firms in total cannot exceed the profit generated in the first place.

For any given cooperative game, there are many possible outcomes. Fundamental research in cooperative game theory focuses on finding outcomes with certain desirable or logical properties. In the following section, we review some desirable properties in which an outcome of a conventional cooperative game can have, assuming that all players choose to cooperate together. While the definition of these properties will be modified later on in our paper, the intuitive meaning behind these properties is still relevant.

### Stability and Core

Assuming that the grand coalition $N$ forms and all participating players choose to cooperate, a stable outcome ensures that any player does not have incentive to leave this grand coalition. In the context of multi-party 