Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour.
A game in normal form is a function: Given the tuple of strategies chosen by the players, one is given an allocation of payments (given as real numbers).
A further generalization can be achieved by splitting the game into a composition of two functions: the outcome function of the game (some authors call this function "the game form"), and: the allocation of payoffs (or preferences) to players, for each outcome of the game.
A game in which players are allowed to form coalitions (and to enforce coalitionary discipline).
Solution concepts for cooperative games usually assume that the players are forming the grand coalition
is then divided among the players to give an allocation.
A simple game is couple (N, W), where W is the list of "winning" coalitions, capable of gaining the loot ('1'), and N is the set of players.