Classes of coalitional game
Superadditive games
Superadditivity is said when the coalitions can work without any sort of interference. This includes both within the group and outside of it.
In such a case, the value of any two coalitions will be no less than the sum of their individual values and the grand coalition will be having the highest payoff.
A game G = (N, v) is said as superadditive, if for all S, T N, if
S T = , then
v(S T) v(S) + v(T)
Convex games
Convex games are too rare in practice and is a stronger condition than superadditivity.
A game G = (N, v) is said as convex, if for all S, T N,
v(S T) v(S) + v(T) – v(S T)
Coalitional Game theory
Coalitional game theory has now become the dominant group of game theory which makes sure of the group preference rather than individual actions. It focuses more on the group than an individual agent as the basic modelling unit. More precisely, we will still be modelling the individual preferences of agents, but definitely not their possible actions. Instead, we would be taking a deep interest in the coarser model of the capabilities of different groups.