Multi-Agent Inference in Social Networks: A Finite Population Approach∗

When people in a society want to make inference about some parameter, each person would potentially want to use data collected by other people. Information (data) exchange in social contexts is usually costly, so to make sound statistical decisions, people need to compromise between benefits and costs of information acquisition. Conflicts of interests and coordination will arise. Classical statistics does not consider people’s interaction in the data collection process. To address this ignorance, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Bearing our interest in aggregate inference at the societal level, we propose a new concept finite population learning to address whether with high probability, a large fraction of people can make “good” inferences. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.