This paper considers distributed systems arising when multiple agents cooperatively solve a quadratic optimisation problem. To maintain privacy of their states over time, agents implement a noise-adding mechanism according to the classic differential privacy framework. We characterise how the noise due to the privacy mechanism degrades the performance of the multi-agent system. Interestingly, we show that depending on the desired level of privacy (and thus noise), the system performance is optimised by reducing the level of cooperation among the agents. The notion of cooperation level, which is formally introduced and defined in the paper, models the trust of an agent towards the information received from neighbouring agents. For the prototypical examples of consensus and centroidal Voronoi tessellations, we are able to characterise the optimum cooperation level that maximises the system performance while ensuring a desired privacy level. Our results suggest that for the class of problems we study, and in fact for a broad class of multi-agent systems, it is always beneficial for the agents to reduce their cooperation level when the privacy level increases.