Reducing the peak energy consumption of households is essential for the effective use of renewable energy sources, in order to ensure that as much household demand as possible can be met by renewable sources. This entails spreading out the use of high-powered appliances such as dishwashers and washing machines throughout the day. Traditional approaches to this problem have relied on differential pricing set by a centralised utility company. But this mechanism has not been effective in promoting widespread shifting of appliance usage. Here we consider an alternative decentralised mechanism, where agents receive an initial allocation of timeslots to use their appliances and can then exchange these with other agents. If agents are willing to be more flexible in the exchanges they accept, then overall satisfaction, in terms of the percentage of agents’ time-slot preferences that are satisfied, will increase. This requires a mechanism that can incentivise agents to be more flexible. Building on previous work, we show that a mechanism incorporating social capital — the tracking of favours given and received — can incentivise agents to act flexibly and give favours by accepting exchanges that do not immediately benefit them. We demonstrate that a mechanism that tracks favours increases the overall satisfaction of agents, and crucially allows social agents that give favours to outcompete selfish agents that do not under payoff-biased social learning. Thus, even completely self-interested agents are expected to learn to produce socially beneficial outcomes.