Presently, renewable power plants participating in electricity markets receive payments at a market price determined by the marginal cost of the marginal generator, generally a conventional power plant. In a market with only renewables, market clearing prices would be determined by the marginal cost of renewable power plants, which is generally close to zero, resulting in capital cost recovery problems for renewable power producers. Hence, in a market with only renewables, a new price-setting mechanism is needed which does not depend on marginal costs. In this paper, we analyze a model of such a mechanism for when all energy production is from renewable power plants such as wind and solar. We consider a mechanism in which producers bid single prices instead of supply functions. While such a price has no physical basis, it enables producers to recover sunk costs and parallels pricing in less regulated, lowmarginal cost industries like software and digital media. We do not advocate the adoption of this mechanism, but rather find it useful for understanding renewable-only markets because it is amenable to analysis of strategic behavior under uncertainty. Specifically, we analyze a game between two renewable producers with random capacities described by arbitrary probability distributions. The producers compete to fulfill a random demand. We find that symmetry (in terms of size/parameters) among producers and variance in producer capacities tend to increase competition. We demonstrate our results via several case studies.