By transforming how transactions are recorded, verified, and arranged, while eliminating the need for intermediaries, blockchain is generating a shift in focus away from centralized structures (e.g., exchanges, trading platforms, energy companies) towards decentralized systems (e.g., end customers, energy consumers interacting directly). In particular, by ensuring security, authenticity, and execution of financial and energy flows of across the grid, blockchain enables organization of electricity consumers with individual ownership of renewable energy resources (such as solar panels) into {\em virtual microgrids} for the purpose of peer-to-peer trading of locally generated renewable energy. In this paper, we develop an analytical framework to describe equilibrium outcomes in such a virtual microgrid whose each heterogeneous participant first decides, at the beginning of the time horizon, on the level of renewable generation capacity to invest in. Then, throughout the time horizon, he satisfies his (stochastic) demand for electricity either from his own installed generation capacity, or by means of blockchain-mediated purchases of electricity available from his peers in the virtual microgrid. We determine the subgame-perfect Nash equilibrium for this two-stage, simultaneous, non-cooperative, infinite-horizon game with perfect information played by participants in a virtual microgrid. For each such participant, we derive: (i) optimal capacity of his renewable energy investment; (ii) optimal amount of energy bought and sold through peer-to-peer electricity trading at each point in time; and (iii) the marginal value of the energy traded in the microgrid that minimizes his electricity-related costs. We prove that an electricity consumer is always better off with a virtual microgrid than without, with his resulting cost savings averaging 9.7\% in our numerical studies. We establish that the cost performance of a virtual microgrid in equilibrium exactly matches that of a centralized microgrid optimized for total cost. Thus, when participants in a virtual microgrid act optimally to minimize their own individual costs, they also achieve full coordination of the entire system and realize its minimum total cost
