The Function form of Game is a part of the cooperative form of game. There are no individual payoffs in this game as one player is able to transfer its utility to the other player. The payoffs are in coalition. The empty coalition is assumed to obtain zero payoff. The seminal book of Von Neumann and Morgenstern talks about this model of game. It assumes that a coalition represented as C plays against a complimentary coalition represented as (N/C), the characteristic is the equilibrium payoff of C. the Function Game is formally referred to as the TU (Total Utility) Game and is represented as a pair (N,v) where N stands for a set of players and v : 2n = R is a characteristic function.
Lastly, the Partition Function form takes into account the way in which the rest of the players are partitioned besides its members while deciding on the coalition payoff.
Types of Games
There are various types of Games. They are:
Cooperative Games where the players from bonds
Symmetric and Asymmetric Game where the payoff one strategy determines payoff of another strategy and not on the players
Zero Sum and Non-Zero Sum where the selection of players do not affect the resources
Simultaneous and Sequential games are game forms where the players move simultaneously
Perfect Information and Imperfect Information where the players either know or do not know the combinations
Infinitely Long Games where the moves are not complete
Economists have successfully applied the Game Theory in analyzing economic phenomenon like bargaining, voting systems, duopolies, fair division, social network, auctions. They follow two methods of application. They are the Descriptive Method and the Prescriptive or Normative method.