On the Usefulness of Cooperation in N Person Games

Abstract

The $N$ person games in which each player maximizes his payoff function are considered. We have studied an interesting question for the cooperative game theory about the usefulness of uniting the $N$ players in a union. The aim of such cooperation is for each player to get a positive increase to his guaranteed payoff. We have obtained some effective sufficient conditions under which the joining of the players in union is useful for each player. The linear case, specially, is being considered. In the second part of the paper, we have studied the question about the usefulness of cooperation of the $N$ players in the presence of the $(N+\mathrm{1})$th player, an ill-intentioned destructive player, whose whole aim is not to win but to harm each player individually, and also the union of these players, for example, global terrorism. It should be noted that the considered situation in the second part is related to A. V. Kryazhimskiy’s talk delivered in the summer of 2014. We obtain constructive conditions under which the union of the players is beneficial in this situation as well.