Multiobjective Optimization

Abstract

In the previous chapters we considered two types of cooperation of the players. In the first case, they form a grand coalition , obtain the largest possible overall payoff which is then divided among the players based on certain concepts of fairness. In the second case the players negotiate to reach a fair settlement. In many cases a third way of cooperation occurs. The players agree in selecting a third person, the mediator , who has the trust of the players and the right and duty of finding a final solution to be given to them. After the mediator reaches his decision, all players are obliged to accept it. In this case, we have a single decision maker, who takes the interests of all players into account simultaneously. If $\phi _1, \ldots , \phi _N$ are the payoff functions of the players and higher value is better for all, then the role of the mediator is to find a satisfactory solution for the corresponding multiobjective optimization problem.