  We study competition and cooperation among a group of storage units. We show
that as the number of storages increases, the profit of storages approaches
zero under Nash competition. We propose two ways in which storages can achieve
non-zero profit and show that they are optimal in the sense that storages
achieve the maximum possible profit. The first is a decentralized approach in
which storages are exposed to artificial cost functions that incentivize them
to behavior as a coalition. No private information needs to be exchanged
between the storages to calculate the artificial function. The second is a
centralized approach in which an aggregator coordinates and splits profits with
storages in order to achieve maximum profit. We use Nash's axiomatic bargaining
problem to model and predict the profit split between aggregator and storages.
