  In economic theory, the concept of externality refers to any indirect effect
resulting from an interaction between players that affects the social welfare.
Most of the models within which externality has been studied assume that agents
have perfect knowledge of their environment and preferences. This is a major
hindrance to the practical implementation of many proposed solutions. To
address this issue, we consider a two-player bandit setting where the actions
of one of the players affect the other player and we extend the Coase theorem
[Coase, 1960]. This result shows that the optimal approach for maximizing the
social welfare in the presence of externality is to establish property rights,
i.e., enable transfers and bargaining between the players. Our work removes the
classical assumption that bargainers possess perfect knowledge of the
underlying game. We first demonstrate that in the absence of property rights,
the social welfare breaks down. We then design a policy for the players which
allows them to learn a bargaining strategy which maximizes the total welfare,
recovering the Coase theorem under uncertainty.
