Positive influence dominating set games

Motivated by applications in social networks, a new type of dominating set named Positive Influence Dominating Set (PIDS) has been studied in the literature. In this paper, we investigate cooperative cost games arising from PIDS problem on social network graphs. We propose two new game models, Rigid PIDS Game and Relaxed PIDS Game, and focus on their cores. First, a relationship between the cores of both games is obtained. Next, we also prove that the core of the relaxed PIDS game is nonempty if and only if there is no integrality gap for the relaxation linear programming of the PIDS problem on graph G.