Non-generating resources (NGRs) such as energy storage and demand response can absorb intermittency from the steadily rising number of wind and solar installations. While there is clear advantage in drawing reserves jointly from NGRs and conventional power sources, there are marked differences between the two, which necessitate new market formats specifically tailored to the characteristics of NGRs. Salient differences from traditional ancillary markets include reduced output duration and faster start-up requirements. In line with the numerous game theoretic analyses of competition in primary generation markets, we analyze strategic behavior between NGRs providing fast regulation in reserve markets. We apply a two-stage framework in which firms first declare capacities and then engage in price bidding; the latter stage is commonly known as Bertrand-Edgeworth competition. We obtain new theoretical results pertaining to equilibrium uniqueness when the demand, in this case energy, is random. By applying the model to energy storage competition, we obtain direct comparisons between two representative market formats based on capacity and energy payments. We find that energy payments may lead to slightly more predictable NGR capacity commitment and reduced regulation energy prices.