This paper consists of two parts. In the first part, we study a centralized rumor blocking problem with a novel social objective function different from those in the literature. We will show that this objective function is non-decreasing and submodular and hence corresponding rumor blocking problem has a greedy approximation with objective function value at least of the optimal. In the second part, we study a decentralized rumor blocking problem with two selfish protectors, which falls into a 2-player non-cooperate game model. We will show that this game is a basic valid utility system and hence the social utility of any Nash equilibrium in the game is at least a half of the optimal social utility.