  We consider a distributed user association problem in the downlink of a small
cell network, where small cells obtain the required energy for providing
wireless services to users through ambient energy harvesting. Since energy
harvesting is opportunistic in nature, the amount of harvested energy is a
random variable, without a priori known characteristics. We model the network
as a competitive market with uncertainty, where self-interested small cells,
modeled as consumers, are willing to maximize their utility scores by selecting
users, represented by commodities. The utility scores of small cells depend on
the amount of harvested energy, formulated as natures' state. Under this model,
the problem is to assign users to small cells, so that the aggregate network
utility is maximized. The solution is the general equilibrium under
uncertainty, also called Arrow-Debreu equilibrium. We show that in our setting,
such equilibrium not only exists, but also is unique and is Pareto optimal in
the sense of expected aggregate network utility. We use the Walras' tatonnement
process with some modifications in order to implement the equilibrium
efficiently.
