  In this paper we study the problem of social learning under multiple true
hypotheses and self-interested agents which exchange information over a graph.
In this setup, each agent receives data that might be generated from a
different hypothesis (or state) than the data other agents receive. In contrast
to the related literature in social learning, which focuses on showing that the
network achieves consensus, here we study the case where every agent is
self-interested and wants to find the hypothesis that generates its own
observations. However, agents do not know which ones of their peers wants to
find the same state with them and as a result they do not know which agents
they should cooperate with. To this end, we propose a scheme with adaptive
combination weights and study the consistency of the agents' learning process.
The scheme allows each agent to identify and collaborate with neighbors that
observe the same hypothesis, while excluding others, thus resulting in improved
performance compared to both non-cooperative learning and cooperative social
learning solutions. We analyze the asymptotic behavior of agents' beliefs under
the proposed social learning algorithm and provide sufficient conditions that
enable all agents to correctly identify their true hypotheses. The theoretical
analysis is corroborated by numerical simulations.
