Multicriteria coalitional game with choice from payoffs

Multicriteria games are model situations in which at least one player has more than one criterion. If we consider that every player is able to assign weights to the criteria, then the situation is simple. In the case of noncooperative games, the game is reduced to a one-criterion classic game. However, in coalitional games one problem remains if the players have different weights: We cannot simplify the vector payoff function to a scalar payoff function. We can analyze the contribution of each player, but it is difficult to analyze the contribution of coalitions. We use the known formulation of linear model that split the gain of the coalition by use of bargaining theory - egalitarian solution. Then we generalize the model for the case when players and coalitions have possibility to choose from more payoffs. We use the binary variables and formulate a mixed integer programming problem. Finally we shall determine the final coalitional structure.