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Journal of Applied Mathematics
Volume 2016 (2016), Article ID 9734615, 5 pages
http://dx.doi.org/10.1155/2016/9734615
Research Article

On the Usefulness of Cooperation in Person Games

1Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, Moscow 119991, Russia
2Department of Mathematics and Computer Science, Faculty of Sciences, Abdou Moumouni University, BP 10662, Niamey, Niger

Received 28 June 2016; Revised 11 September 2016; Accepted 26 September 2016

Academic Editor: Bo Yu

Copyright © 2016 Mikhail Sergeevich Nikolskii and Aboubacar Moussa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The 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 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 players in the presence of the 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.