In current power markets, the bulk of electricity is sold wholesale and transported to consumers via long-distance transmission lines. Recently, decentralized local energy markets have evolved, often as isolated networks based on solar generation. We analyze strategic pricing, investment, and welfare in local energy markets. We show that local energy markets yield competitive equilibrium prices and provide efficient investment incentives. Yet, we find that strategic behavior leads to allocative inefficiency. We propose a clearing mechanism that induces truth-telling behavior and restores first-best welfare.