Mechanism Design for Collaborative Normal Mean Estimation

We study collaborative normal mean estimation, where m strategic agents collect i.i.d samples from a normal distribution \mathcal{N}(\mu, \sigma 2) at a cost. They all wish to estimate the mean \mu . By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes.