Local energy markets (LEMs) are well suited to address the challenges of the European energy transition movement. They incite investments in renewable energy sources (RES), can improve the integration of RES into the energy system, and empower local communities. However, as electricity is a low involvement good, residential households have neither the expertise nor do they want to put in the time and effort to trade themselves on their own on short-term LEMs. Thus, machine learning algorithms are proposed to take over the bidding for households under realistic market information. We simulate a LEM on a 15 min merit-order market mechanism and deploy reinforcement learning as strategic learning for the agents. In a multi-agent simulation of 100 households including PV, micro-cogeneration, and demand shifting appliances, we show how participants in a LEM can achieve a self-sufficiency of up to 30% with trading and 41,4% with trading and demand response (DR) through an installation of only 5kWp PV panels in 45% of the households under affordable energy prices. A sensitivity analysis shows how the results differ according to the share of renewable generation and degree of demand flexibility.