In this paper, we propose a co-opetitive mean-field-type game (MFTG) approach in which decision makers interact with each other by means of partial cooperation and competition simultaneously. The proposed novel approach allows decision makers' preferences to evolve over time to cooperate with those who contribute to their utilities, and to compete with those who are working against their individual interests. In addition, we consider that each decision maker has a co-opetitive capacity/power. The co-opetitive MFTG involves concepts, such as selfishness, altruism, competition, cooperation, among others; all together within the same strategic interaction. Both co-opetitive MFTGs and evolutionary dynamics describing the evolution of co-opetitive parameters are combined. We design incentives to promote the emergence of co-opetition over selfish behavior.