Cooperative $n$-person prisoner's dilemma on a network

In the paper $n$-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the influence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.