So we all know about non-cooperative game theory: it’s every man for himself. But, cooperative game theory has some interesting applications. The difference between the two is that cooperative game theory has groups or coalitions that enforce players to cooperate. Every possible coalition that can be formed gives a payoff to the players who form the coalition. Usually, a restriction is put in place: by adding more people to a possible coalition, you cannot decrease the payoff (though you may decrease they payoff per person). The first concept for CGT that was similar to the Nash Equilibrium for NCGT was the idea of a stable set. A stable set is a set that satisfies two properties:

1) There cannot be a coalition in the set that dominates another coalition

2) Every coalition outside the set is dominated by some coalition inside the set

Unfortunately, these do not always exist, nor are they unique. Thus, other similar concepts have been developed, such as the core, shapley value, or the kernel of a game.

It seems like cooperative games would develop in many social situations where we wouldn’t necessarily expect a game to exist. Forming project teams seems to be a situation where different coalitions would give different values. Different team members might work well together, so payoffs would not be boring.