Despite the well‐established importance of team composition, there has been relatively little research that focuses on compositions regarding problematic personality traits. This study examines the impact of Machiavellianism, narcissism, psychopathy, and sadism—all operationalized as team composition variables—on team cooperation and performance over time. This was done in a sample of 43 graduate student teams (n = 269) engaged in an immersive business simulation that unfolded over a 6‐week duration. In addition, the parameters of the simulation task were altered midway through the simulation without forewarning, in turn creating a shock event that allowed for an examination of whether team composition for negative personality had similar effects under conditions of business‐as‐usual versus a disruptive change. Results indicated that both team average Machiavellianism and sadism had deleterious effects on team cooperation and performance over time, while controlling for two closely associated positive personality traits (honesty‐humility and agreeableness). These damaging effects were further revealed to especially detract from performance trajectories after teams experienced a disruptive event. Overall, our findings highlight the importance of including problematic personality traits in considerations pertaining to team composition.