Predictions often influence the reality which they aim to predict, an effect known as performativity. Existing work focuses on accuracy maximization under this effect, but model deployment may have important unintended impacts, especially in multiagent scenarios. In this work, we investigate performative prediction in a concrete game-theoretic setting where social welfare is an alternative objective to accuracy maximization. We explore a collective risk dilemma scenario where maximising accuracy can negatively impact social welfare, when predicting collective behaviours. By assuming knowledge of a Bayesian agent behavior model, we then show how to achieve better trade-offs and use them for mechanism design.