We introduce a coalition welfare game model with a group of homogeneous players who have the same characteristics. In this coalition model, the players’ preferences are described by a class of utilities that are used to construct a quadratic welfare function. We derive three main welfare thresholds to distinguish the players’ preferences when they adapt a certain behavior. We determine all optimal welfare strategies in this coalition game and distinguish between the pure and mixed optimal welfare strategies. We use geometry to show the existence of hysterical dynamics in the players’ behaviors under certain values of the influence parameter. Finally, we determine the maximum welfare occurrence based on the type of the welfare strategies.